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1 ( x, T ( x, T = D t T, x, t, (1-1) x D T T HP 005 HP 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

2 ( 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( ) /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

3 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 Octave Octave-forge 1. 0 MATLAB Help MATLAB 93

4 0 λ 1 λ λ = 1 6 N N λ 1 4,

5 1 50 C 1.75cm s 1 10 cm t = 0 s 30 C 95

6 \ \ \ \ \ \ \ \\ 96

7 \ \\ x 0 < λ 1 λ = D T x for for Previous C Octave Octave 97

8 T / deg : t= s 1000: t= s 000: t= s 3000: t=.8571 s 4000: t= s 5000: t= s 6000: t= s 7000: t= s 8000: t= s 9000: t= s 10000: t= s 11000: t= s 1000: t= s 13000: t= s 14000: t= s 15000: t= s 16000: t= s 17000: t= s 18000: t= s 19000: t= s 0000: t= s 1000: t= s 000: t=0.954 s 3000: t= s 4000: t=.8571 s 5000: t= s 6000: t= s 7000: t= s 8000: t= s 9000: t= s 30000: t= s x / cm λ = : t= s : t= s T / deg 40 T / deg x / cm x / cm λ 1 λ = D T x x λ 98

9 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

10 \ \ \ \ \ \ \ \ 100

11 \\ \ \ \\ T / deg 50 0: t= s 5: t= s 10: t= s 15: t= s 0: 45 t= s 5: t= s 30: t= s 35: t= s 40: t= s 45: 40 t= s 50: t= s 55: t= s 60: t= s 65: t= s 35 70: t= s 75: t= s 80: t= s 85: t= s 90: t= s 95: t= s 100: t= 0.09 s 105: t= s 110: t= s 115: t= s 10: t= s 15: t= s 130: t= s 135: t= s 140: t= s 145: t= s 150: t= s 155: t= s 160: t= s 165: t= s 170: t= s 175: t= s 180: t= s 185: t= s 190: t= s 195: t= s 00: t= s x / cm 101

12 10

13 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