資料

Transcription

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3 PC

4 PC C

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15 VMwareをインストールする

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18 Tips: VmwareFusion *.vmx vhv.enable = TRUE

19 Tips: Windows Hyper-V

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33 -rwxr-xr-x 1 masakazu staff :18 a.out* -rw masakazu staff :18 a.out

34 d r w x r w x r w x directory

35 Destroy your PC...

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38 $: gnuplot

39 $: plot sin(x) OK!

40 Exercise Exercise

41 Exercise Exercise x*x x**8 exp(x)

42 $: plot sin(x), cos(x)

43 $: plot [-1:2] sin(x),cos(x) $: plot [-1:2][-3:4] sin(x),cos(x)

44 $: splot x**2-y**2 google

45 data.txt x y1 y2 gnuplot $: plot "data.txt"

46 $: plot "data.txt" with lines $: plot "data.txt" using 1:3 with lines $: plot "data.txt" using 1:3 with lines, "data.txt" using 1:2 with lines

47 Tips!! $: plot "data.txt" using 1:3 with lines, "data.txt" using 1:2 with lines $: plot "data.txt" u 1:3 w l, "data.txt" u 1:2 w l

48 4_Gnuplot_1.c #include <stdio.h> int main(void) double x,y; double L = 1.0; //x length int N = 4; //Bunkatu double dx = L / N; //kizami int i; for(i = 0;i < N;i ++) x = (i + 0.5) * dx; y = x * x; printf("%f %f\n",x,y); return 0;

49 > gnuplot Exercise N L

50 4_Gnuplot_2.c

51 4_Gnuplot_2.c

52 #include <stdio.h> #include <math.h> int main(void) double x,y,z; double Lx = 2.0; //x length double Ly = 2.0; //y length int Nx = 4; //x Bunkatu int Ny = 4; //y Bunkatu double dx = Lx / Nx; //x kizami double dy = Ly / Ny; //y kizami for(int i = 0;i < Nx;i ++) for(int j = 0;j < Ny;j ++) x = (i + 0.5) * dx - Lx / 2; y = (j + 0.5) * dy - Ly / 2; z = x * x - y * y; printf("%f %f %f \n",x,y,z); printf("\n"); return 0; 4_Gnuplot_2.c gnuplot 4x4 gnuplot 40x40

53 Exercise

54 Exercise

55 x t

56 x t C gnuplot

57 C #include <stdio.h> int main(void) FILE *gp;//for gnuplot gp = popen("gnuplot -persist","w"); fprintf(gp, "set terminal x11\n"); fprintf(gp, "plot sin(x)\n"); fflush(gp); pclose(gp); return 0; 4_Gnuplot_3.c

58 C #include <stdio.h> #include <math.h> int main(void) int i; int N = 40; double x,y; double L = 2 * ; double dx = L / N; gnuplot FILE *gp;//for gnuplot gp = popen("gnuplot -persist","w"); fprintf(gp, "plot '-' with lines \n");// for(i = 0;i < N;i ++) x = (i + 0.5) * dx; y = sin(x); fprintf(gp,"%f %f\n", x, y);// fprintf(gp,"e\n"); // fflush(gp); pclose(gp); return 0; 4_Gnuplot_4.c

59 C #include <stdio.h> #include <math.h> int main(void) int i; int i_time; int N = 40; double x,y; double L = 4 * ; double dx = L / N; double dt = 0.05; FILE *gp;//for gnuplot gp = popen("gnuplot -persist","w"); fprintf(gp, "set terminal x11\n"); for(i_time = 0;;i_time ++) fprintf(gp, "set yrange [-1.2:1.2]\n"); fprintf(gp, "plot '-' with lines \n"); for(i = 0;i < N;i ++) x = (i + 0.5) * dx; y = sin(x - i_time * dt); fprintf(gp,"%f %f\n", x, y); fprintf(gp,"e\n"); fflush(gp); pclose(gp); gnuplot Tips! Ctrl + C return 0; 4_Gnuplot_5.c

60 Exercise

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69 Euler

70 Euler Euler

71 Euler Euler

72 Euler Euler

73 Euler Euler

74 Euler #include <stdio.h> #include <math.h> int main(void) int i; double dt = 0.01; double xn,xn_new; FILE *gp; gp = popen("gnuplot -persist","w"); fprintf(gp, "set terminal x11\n"); fprintf(gp, "set yrange[-1.1:1.1] \n"); fprintf(gp, "plot '-' with lines \n"); xn = 0; for (i = 0; i < 1000; i++) fprintf(gp,"%f %f\n", i * dt, xn);// xn_new = xn + dt * cos(i * dt);// xn = xn_new; fprintf(gp,"e\n"); fflush(gp); pclose(gp); return 0; 5_ODE_1.c gnuplot gnuplot

75 Exercise 5_ODE_2.c 5_ODE_3.c 5_ODE_4.c

76 a=0 のとき以外はいつも 1 に向かう. なぜだろう?

77 小さの勝負表 と置く. ただしの小さい数とする. を代入する. ε ε= ε 2 x(t) ε= ε= 傾きはε t t=0 つまり時刻 t=0での傾きは正なので, ちょっと先の未来では, 少なくとも値は増える. つまり, a=0 から離れていく! ε= 一兆円 (10^12) の前では 100 万円 (10^6) はゴミでしょ?

78 C Code #include <stdio.h> #include <math.h> int main(void) int i; double dt = 0.01; double xn,xn_new; double yn,yn_new; xn = 1.0; yn = 0.0; for (i = 0; i < 1000; i++) printf("%f %f %f\n",i * dt, xn, yn); xn_new = xn + dt * (-yn); yn_new = yn + dt * (xn); xn = xn_new; yn = yn_new; return 0; 5_ODE_5.c

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81 dt

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85 δ θ δ θ

86 δ θ δ θ

87 δ θ δ θ

88 δ θ δ θ

89 δ θ δ θ

90 δ θ δ θ

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92 3δ 2δ δ 0 δ 2δ 3δ τ δ

93 I n i x i (n) δ +δ x i (n 1) x i (n) = x i (n 1) ± δ I n x(n) = 1 I x i (n) i=1 x(n) x(n 1) x(n) = 1 I I (x i (n 1) ± ) = 1 I I x i (n 1) = x(n 1) i=1 i=1

94 x(0) = 0 x(n) = 0 n x(n) 2 x(n) 2 = 1 I I i=1 x i (n) 2 x i (n) 2 = x i (n 1) 2 ± 2 x i (n 1) + 2 x(n) 2 = x(n 1) 2 + δ 2 = x(n 2) 2 + 2δ 2 = = x(0) 2 + nδ 2 x(n) 2 = nδ 2

95 t x(n) 2 = nδ 2 t = τn x(t) 2 = δ2 τ t D = δ2 2τ x(t) 2 = 2Dt σ(t) σ(t) = 2Dt D [D] = L 2 T 1

96 2Dt

97 2Dt

98 10 5 m 2 /sec

99 10 5 m 2 /sec

100 10 5 m 2 /sec t = (t)2 2D = = sec 2 month

101 t t t t

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sha1_base64="mi/cyog9sbevcpa1/kyvpu42kke=">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</latexit> ui <latexit sha1_base64="+p4wkmu+ulzbfq0nxbxpbdjq2/g=">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</latexit> ui+1 Fickの法則 温度の勾配に比例して物理量が伝播する <latexit sha1_base64="yfbvauvgtc+64al2yvshyixq0z4=">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</latexit> ui x ui x = t Di+1/2 ( ui+1 ui x ) Di 1/2 ( ui ui x 1 )

106 <latexit sha1_base64="c3x1chgyc1c5xgvnypnlims7ybo=">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</latexit> <latexit sha1_base64="zqfmdetenbm7+o4a0azdskgjuh8=">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</latexit> t=0 <latexit sha1_base64="xcitd5bcjtafucxhfy063d0z0wq=">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</latexit> x x <latexit sha1_base64="c3x1chgyc1c5xgvnypnlims7ybo=">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</latexit> <latexit sha1_base64="c3x1chgyc1c5xgvnypnlims7ybo=">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</latexit> x ui 1 ui ui+1 6度 ４度 10度 <latexit sha1_base64="urtx2erpnssnkepwwwdun4dulw0=">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</latexit> <latexit sha1_base64="o0gq0tlgf3f7ifempypvyeef8yu=">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</latexit> Di Di+1/2 1/2 <latexit sha1_base64="80hmfmi4v3amxclnqnr9ge9/tyy=">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</latexit> <latexit sha1_base64="usdjrnobdn+mmek+pcyeh4y/jd4=">aaacyxichvfnsxtrfd1oa6vw1thubdfbxnjvufmes0equymi4fcsmqlhzvksds68mc68xi/qvxddcy5eqael8wd00z/gwp8gli1004v3xoawgmzfmo/dd 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sha1_base64="kc2cylf+cm8iwn96rvvj8zssa0w=">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</latexit> t= t <latexit sha1_base64="fjql78akc8uekk6lfjgwxbwnqka=">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</latexit> <latexit sha1_base64="yfbvauvgtc+64al2yvshyixq0z4=">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</latexit>?度 ui x ui 1 <latexit sha1_base64="mi/cyog9sbevcpa1/kyvpu42kke=">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</latexit> ui <latexit sha1_base64="+p4wkmu+ulzbfq0nxbxpbdjq2/g=">aaacxnichvfnsxxbeh1oyvyizjfjrfcyuboeyakjayonxvz2elg1uyuyzzkzw22c6rnmy3udhjxzyykqtwl4cpkzueqpenifib5xycwh1pqoervjd9nd/apedb0qo3blfbp1r4whd0cfjy1ptd6emn5skd591oz8jhrew/fdp9y0rui4uolglgnxbaahsdzbfs17/03mb3vfgelfvyt7gwh71q6so9kxyozassevs+zxp1imculvum2yuvfgvup+8qzvsq0fdhj4efci2xzhiejvcyyiawntpiyfbentfzjgjhmtjhicytg6z/su37zyvpe9yxlptsovupyhzcxhgc7oow3of/2gc/pzz65u58hq6ffpd7ki6bq+zmz8vpfl8rlj74r135pj7oc1rlvy7yfgmhxokn89+jzywflfsf/qn7rg+r9sn36yatw9de7xxpqjzq6yc6dvevp9xf1ngx/lcprsy7jlfw1rnnpk41dbtu7q9r+qs5hhmspnmchd5ugan0d522i+rjhumddelaur+zjhmys5lhkmzvrrqx0nrfwtvudeqbnksiydyagxknoe49oypvwfbewexq==</latexit> ui+1 10度 ４度 ４度 ui+1 ui ui x = t Di+1/2 ( ) x 正の符号 ４度 6度 ui ui 1 Di 1/2 ( ) x 負の符号

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108

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sha1_base64="0cbxrtgxbpnj/gpryb2udrlyd3q=">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</latexit> u i = Dr 2 u u i u i = D x 2 (u i+1 2u i u i 1 ) t U(x + x) =U(x)+ U 0 (x) 1! U 0 (x) U(x x) =U(x) 1! x + U 00 (x) 2! x + U 00 (x) 2! x 2 + U 000 (x) 3! x 2 U 000 (x) 3! x 3 + O( x 4 ) x 3 + O( x 4 ) U(x + x)+u(x x) =2U(x)+U 00 (x) x 2 + O( x 4 ) U (x) = U(x δx) 2U(x) + U(x + δx) δx 2 + O(δx 2 )

110 u 2 t = D u x 2 u(x, t + t) u(x, t) t D u(x x, t) 2u(x, t)+u(x + x, t) x 2 u n+1 i δt u n i = D un i 1 2un i + un i+1 δx 2 t (i = 1, 2,, I; n = 0, 1, ) x

111 u n 0,u n I+1 u n 0 u n I+1 u n 1 u n I l u n 0 + u n 1 2 u(0,t n )=0, u n I + un I+1 2 u(, t n )=0 u n 0 = u n 1, u n I+1 = u n I

112 l u n 1 u n 0 x u x (0,t n)=0, u n I+1 x u n I u x (, t n)=0 u n 0 = u n 1, u n I+1 = u n I l I I I+ 1 u n 0 = u n I, u n I+1 = u n 1

113 u n+1 i u n i δt = D un i 1 2un i + un i+1 δx 2 (i = 1, 2,, I; n = 0, 1, ) u n 0 = u n 1, u n I+1 = u n I u n 0 = u n 1, u n I+1 = u n I u n 0 = u n I, u n I+1 = u n 1 (n = 0, 1, ) u 0 i = f(x i ) (i = 1, 2,, I)

114 u n+1 i u n i δt = D un i 1 2un i + un i+1 δx 2 (i = 1, 2,, I; n = 0, 1, ) u n 0 = u n 1, u n I+1 = u n I u n 0 = u n 1, u n I+1 = u n I u n 0 = u n I, u n I+1 = u n 1 (n = 0, 1, ) u 0 i = f(x i ) (i = 1, 2,, I)

115 u n+1 i u n i δt = D un i 1 2un i + un i+1 δx 2 λ = Dδt δx 2 u n+1 i = u n i + λ(u n i 1 2u n i + u n i+1) n + 1 n i 1 i + 1 i

116 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

117 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

118 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

119 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

120 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

121 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

122 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

123 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

124 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

125 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

126 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

127 #include <stdio.h> #include <stdlib.h> #include <math.h> #define Imax (100) #define PI ( ) #define L (2.0 * PI) #define INTV (10) double f(double x) double ans; ans = cos(3 * x); //ans = rand() / ((double)rand_max); return ans; int main(void) int i,i_time; FILE *gp; gp = popen("gnuplot -persist","w"); //fprintf(gp,"set terminal x11\n"); fprintf(gp,"set terminal aqua\n"); fprintf(gp,"set xrange[0:%f]\n",l); fprintf(gp,"set yrange[-2:2]\n"); double u[imax + 2]; double u_new[imax + 2]; double x,y; double dx = L / Imax; double dt = ; double D = 0.01; double lambda = D * dt / (dx * dx); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; u[i] = f(x); for(i_time = 0;;i_time ++) if(1) double sum = 0.0; for(i = 1;i <= Imax;i ++) sum += u[i] * dx; printf("%15.15f\n",sum); //B.C. u[0] = u[1]; u[imax + 1] = u[imax]; //plot if(i_time % INTV == 0) fprintf(gp,"plot '-' with lines\n"); for(i = 1;i <= Imax;i ++) x = (i - 0.5) * dx; y = u[i]; fprintf(gp,"%f %f\n",x,y); fprintf(gp,"e\n"); fflush(gp); //Calc Eq for(i = 1;i <= Imax;i ++) u_new[i] = u[i] + lambda * (u[i - 1] - 2 * u[i] + u[i + 1]); //Subs for(i = 1;i <= Imax;i ++) u[i] = u_new[i];

128

129 u t = D 2 u x 2 u u (0, t) = (l, t) = 0 x x u(x, 0) = f(x) for 0 < x < l, t > 0 for t > 0 for 0 < x < l l u udx d dt l 0 udx = l 0 0 u t dx = l 0 D 2 u u dx = D x=l x2 x x=0 = 0

130

131 u v

132 u v

133 u v

134 u v

135 u v

136 u v

137 u v u v

138 u v u v u v u v + +

139 du dt = u(1 u2 ) v dv dt =3u 2v

140 du dt = u(1 u2 ) v dv dt =3u 2v v u

141 du dt = u(1 u2 ) v dv dt =3u 2v (0, 0) A v u

142 du dt = u(1 u2 ) v dv dt =3u 2v (0, 0) A [ ] 1 1 A = 3 2 v u

143 du dt = u(1 u2 ) v dv dt =3u 2v (0, 0) A [ ] 1 1 A = 3 2 v u tra = 1 deta = 1

144 du dt = u(1 u2 ) v dv dt =3u 2v (0, 0) A [ ] 1 1 A = 3 2 v u tra = 1 deta = 1 (0, 0)

145 du dt = u(1 u2 ) v dv dt =3u 2v (0, 0) A [ ] 1 1 A = 3 2 v u tra = 1 deta = 1 (0, 0)

146 du dt = u(1 u2 ) v dv dt =3u 2v (0, 0) A [ ] 1 1 A = 3 2 tra = 1 deta = 1 v deta u tra (0, 0)

147 = = D u(1 u2 ) u 2v on R

148 = = D u(1 u2 ) u 2v on R (u, v) (0, 0)

149 = = D u(1 u2 ) u 2v on R (u, v) (0, 0) (0, 0)

150 = = D u(1 u2 ) u 2v

151

152

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154 ) ( u(x, t) ( 0 0 ) ) v(x, t) = + δ ( ϕ(x, t) ψ(x, t) δ 1

155 ( u(x, t) ) ( 0 0 ) ( ϕ(x, t) ) v(x, t) = + δ ψ(x, t) δ 1 ϕ t = D u 2 ϕ x 2 + ϕ ψ ψ t = D v 2 ψ + 3ϕ 2ψ x2

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sha1_base64="np7msylhaixtbjhl4xiuklgfld4=">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</latexit> = e kt cos(m x/l x ) 0 = e kt cos(m x/l x ) 0 k := m /L x

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sha1_base64="np7msylhaixtbjhl4xiuklgfld4=">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</latexit> <latexit sha1_base64="np7msylhaixtbjhl4xiuklgfld4=">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</latexit> = e kt cos(m x/l x ) 0 = e kt cos(m x/l x ) 0 λ k ( ϕ0 ψ 0 ) = ( 1 Du k D v k 2 ) ( ϕ0 ψ 0 ) k := m /L x

158 <latexit sha1_base64="kgffcapote6gaod6slpsvbnbwr8=">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</latexit> <latexit 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sha1_base64="kgffcapote6gaod6slpsvbnbwr8=">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</latexit> <latexit sha1_base64="w/5oc0q8e1nnqmpnlamaoaatzyo=">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</latexit> <latexit sha1_base64="w/5oc0q8e1nnqmpnlamaoaatzyo=">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</latexit> <latexit sha1_base64="w/5oc0q8e1nnqmpnlamaoaatzyo=">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</latexit> <latexit sha1_base64="w/5oc0q8e1nnqmpnlamaoaatzyo=">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</latexit> <latexit sha1_base64="np7msylhaixtbjhl4xiuklgfld4=">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</latexit> <latexit sha1_base64="np7msylhaixtbjhl4xiuklgfld4=">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</latexit> <latexit sha1_base64="np7msylhaixtbjhl4xiuklgfld4=">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</latexit> <latexit sha1_base64="np7msylhaixtbjhl4xiuklgfld4=">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</latexit> ϕ t = D u 2 ϕ x 2 + ϕ ψ = e kt cos(m x/l x ) 0 ψ t = D v 2 ψ + 3ϕ 2ψ x2 = e kt cos(m x/l x ) 0 λ k ( ϕ0 ψ 0 ) = ( 1 Du k D v k 2 ) ( ϕ0 ψ 0 ) k := m /L x

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162

163

164 <latexit sha1_base64="w+vuognnmit8wdljffzudh2bugi=">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</latexit> <latexit sha1_base64="w+vuognnmit8wdljffzudh2bugi=">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</latexit> <latexit sha1_base64="w+vuognnmit8wdljffzudh2bugi=">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</latexit> <latexit sha1_base64="w+vuognnmit8wdljffzudh2bugi=">aaac03ichvflsxxbep4cnze+nnojeflcdephrqmbqcejfw8kprkr4c7lzgyrjfniznzdm+qspamepqhcamkcpyox/aep/osqo4fcpfjto0ru1b6mu/qr+qq/qjj9w4yr0wwl1trw3thz9al7zu9vx3/m1uax9gqbjqqwz3vbummewpaukeqyssw6hwjdmw2xzu7mjf61ughc6bkfoz1flb1jy5wb0jiihiqzgzllhwp69etjlxonyyvky7ysyvge1mo+nptuycfds17maivu4cfcdq4exers2zaq8rcbhqsfstjixgk2ppilfey3c2scjtjcyhsh9y2+basoy/ckz6jyfr9i8x8wm4truqafdew/6jx+0/wjuwkvi9gyx6fz5aq/0n/wevxfsyyhzwjbt6wnnufyxjtsklm7r5ckcqvjr386ulqdwrmn39a3+sp6v9il/eqk3ppf63rzrbyr7c5zdlw1jnrf5f7gjc9ybux2jdmsvpyvmttkoafsu3wo+l91fipiceqim7jbpfz9/igfgsw3ez3y+vk73oyhdmxdgmiwxjjte8xihksosiogtncg71pbi7uv2n4zvgtjoyo4s7tdg7ruoho=</latexit> cos(19 x/l x )

165 = = D u(1 u2 ) u 2v

166 2Dシミュレーター デフォルト値 ある値で

167 2Dシミュレーター デフォルト値 ある値で

168 2Dシミュレーター デフォルト値 ある値で