( x, T ( x, T = D t T, x, t, (1-1) x D T T HP 005 HP http://www.nuce.nagoyau.ac.jp/e8/matsuoka/mathce/05mathce.html 10/18 T ( x, 0) = Ti ( x) (1-) T ( 0, = Tb0( T ( l, = Tbe ( (1-3) 1 Dirichlet Excel Octave (1-1) << 1 f x Taylor h ( ) h f ( x ± h) f ( x) ± hf ( x) + f ( x) + (1-4) f ( ) ( x + h) f ( x) f x (1-5) h f ( ) ( x + h) f ( x) + f ( x h) f x (1-6) h (1-5) (1-6)(1-1) 91
( x, t + ) T( x, T ( x +, T ( x, + T ( x, T DT (1-7) λ = D T (1-8) (1-8) T ( x, t + ) = λ T ( x +, + ( 1 λ) T ( x, + λt ( x, (1-9) t t + = l N T n, m n = 1,, N, N + 1 : m = 1,,, T n, m = T (( n 1), ( m 1) ) (1-10) (1-9) T n, 1 = λ Tn + 1, m + ( 1 λ) Tn, m + λtn 1, m (1-11) (1-), (1-3) T n, 1 = Ti (( n 1) ) (1-1) T m = T (( m 1) T = T (( m ) + (1-13) (1-13) (1-11) n =, 3, N 1, b0 N 1, m be 1 (1-8) λ = 0 < λ 1 n m D T 0 λ > 1 (1-11) λ 0 < λ 1 λ > 1 (1-11) ( 1 λ) T n, m 4 6 λ = 1 6 O( ) O( ) 005 11/8 λ λ = 1 λ = 1 (1-11) = (1-14) T ( T T ) n, 1 n+ 1, m + n 1, m 6 = 1 λ (1-11) Octave Octave MATLAB Scilab (1-11) T, 9
T1, 1 a T m 1, m T, 1 λ 1 λ λ T, m = Tn, 1 λ 1 λ λ Tn, m (1-15) T N,! λ 1 λ λ TN, m TN + 1, 1 bm TN, m T1, 1 TN + 1, 1 a m, b m a m = b m = 1 0 (1-11) 0 0 Band MatrixOctave-.1.50 Octave-.1.50 Octave-forge 1. 0 MATLAB Help MATLAB 93
0 λ 1 λ λ = 1 6 N N 3 1 1 λ 1 4,5 3 3 4 94
1 50 C 1.75cm s 1 10 cm t = 0 s 30 C 95
\ \ \ \ \ \ \ \\ 96
\ \\ x 0 < λ 1 λ = D T x for for Previous C Octave.9.1.9.1 Octave 97
T / deg 50 45 40 35 0: t= 0.0000 s 1000: t= 0.954 s 000: t= 1.9048 s 3000: t=.8571 s 4000: t= 3.8095 s 5000: t= 4.7619 s 6000: t= 5.7143 s 7000: t= 6.6667 s 8000: t= 7.6190 s 9000: t= 8.5714 s 10000: t= 9.538 s 11000: t=10.476 s 1000: t=11.486 s 13000: t=1.3810 s 14000: t=13.3333 s 15000: t=14.857 s 16000: t=15.381 s 17000: t=16.1905 s 18000: t=17.149 s 19000: t=18.095 s 0000: t=19.0476 s 1000: t=0.0000 s 000: t=0.954 s 3000: t=1.9048 s 4000: t=.8571 s 5000: t=3.8095 s 6000: t=4.7619 s 7000: t=5.7143 s 8000: t=6.6667 s 9000: t=7.6190 s 30000: t=8.5714 s 30 0 4 6 8 10 x / cm λ = 1 + 0. 001 50 1300: t= 3.717 s 50 1900: t= 5.4394 s 45 45 T / deg 40 T / deg 40 35 35 30 0 4 6 8 10 x / cm 30 0 4 6 8 10 x / cm λ 1 λ = D T x x λ 98
T ( x, t + ) T ( x, T ( x +, t + ) T ( x, t + ) + T ( x, t + ) DT (1-16) (1-7) T ( x, t + ) T ( x, T ( x +, T ( x, + T ( x, DT (1-17) t t + λ T ( x +, t + ) + ( 1+ λ) T ( x, t + ) λt ( x, t + ) = T ( x, (1-18) (1-10) T n, m = T (( n 1), ( m 1) ) (1-19) λ T n+ 1, 1 + ( 1 + λ) Tn, 1 λtn 1, 1 = Tn, m (1-0) T n, 1 = Ti (( n 1) ) (1-1) T m = T (( m 1) T = T (( m ) 1, b0 + (1-) N 1, m be 1 (1-0) a T m 1, 1 T1, m λ 1 + λ λ T, 1 T, m = λ 1 + λ λ Tn, 1 Tn, m (1-3) λ 1 + λ λ T N,! TN, m bm TN + 1, 1 TN, m a m, b m a m b = 1 { T, } { T } n m n, 1 = m {T i,j+1 } {T i,j+1 }{T i,j } {T i,j+1 }{T i,j } (1-3).1.50 octave-forge octave-forge λ x 99
\ \ \ \ \ \ \ \ 100
\\ \ \ \\ T / deg 50 0: t= 0.0000 s 5: t= 0.0011 s 10: t= 0.003 s 15: t= 0.0034 s 0: 45 t= 0.0046 s 5: t= 0.0057 s 30: t= 0.0069 s 35: t= 0.0080 s 40: t= 0.0091 s 45: 40 t= 0.0103 s 50: t= 0.0114 s 55: t= 0.016 s 60: t= 0.0137 s 65: t= 0.0149 s 35 70: t= 0.0160 s 75: t= 0.0171 s 80: t= 0.0183 s 85: t= 0.0194 s 90: t= 0.006 s 95: t= 0.017 s 100: t= 0.09 s 105: t= 0.040 s 110: t= 0.051 s 115: t= 0.063 s 10: t= 0.074 s 15: t= 0.086 s 130: t= 0.097 s 135: t= 0.0309 s 140: t= 0.030 s 145: t= 0.0331 s 150: t= 0.0343 s 155: t= 0.0354 s 160: t= 0.0366 s 165: t= 0.0377 s 170: t= 0.0389 s 175: t= 0.0400 s 180: t= 0.0411 s 185: t= 0.043 s 190: t= 0.0434 s 195: t= 0.0446 s 00: t= 0.0457 s 30 0 4 6 8 10 x / cm 101
10
Octave 004 Octave Octave Octave Octave liboctave C++ C++ Octave liboctave C++ Octave Octave Octave Octave Octave Octave Octave Octave Ver. Ver..9 MATLAB Octave UNIX Microsoft C++Windows Native Octave Windows Octave 007 7 13 103