微分方程數(shù)值計(jì)算方法

1、 舉個(gè)例子： 熱源B: Tw2=50 oC 熱源A: Tw1=100oC 熱源A: Tw1=100oC 熱源B: Tw2=50 oC n +1 n n n n n Ti， （ 1 - 4 f ）Ti， ， 2， L；i = 1， 2,.; j = 1, 2,.） j = fTi -1，j + fTi，j -1 + j + fTi +1，j + fTi，j +1 （n = 1 0 2.; j = 1, 2,.） Ti , j = T0 （i = 1， n n n n L） 2， Ti =0 = Ti = m = Tw1 ； T j =0 = T j = m = Tw 2 （n = 1， 2D T

2、emperature Field, t=0s fwdfb2d.m程序示例:(穩(wěn)態(tài)情況 clear; close all; L=100; M=20; timeMax=50000; Currtime = 100; DL=0:L/M:L; T = ones(M,M,timeMax*30; T(1:M,1,1:1:timeMax=100; T(1:M,M,1:1:timeMax=100; T(1,1:M,1:1:timeMax=50; T(M,1:M,1:1:timeMax=50; f=0.3; for t=2:timeMax for i=2:M-1 for j=2:M-1 T(i,j,t=f*T(i

3、-1,j,t-1+f*T(i,j-1,t +(1-4*f*T(i,j,t-1 +f*T(i+1,j,t-1+f*T(i,j+1,t-1; end; end; end; x,y=meshgrid(1:M,1:M; mesh(x,y,T(1:M,1:M,Currtime; title(2D Temperature Field, t=,num2str(Currtime-1,s; xlabel(x length(L/M; ylabel(y length(L/M; zlabel(Temperature(oC; 100 90 80 70 60 50 40 20 Temperature(oC 15 10 5

4、 y length(L/M Temperature(oC 100 80 60 40 20 20 15 10 5 y length(L/M 0 0 5 x length(L/M 15 10 20 2D Temperature Field, t=9s 100 2D Temperature Field, t=39s Temperature(oC 80 60 40 20 20 15 10 5 y length(L/M 0 0 10 5 x length(L/M 15 20 20 15 10 5 0 0 x length(L/M 100 90 Temperature(oC 80 70 60 50 20 15 10 5 y len