偏微分差分四种格式的matlab程序 (2).pdf
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偏微分差分四种格式的 matlab 程序
偏微分差分四种格式的 matlab 程序
（1）Lax-Fridrichs 格式
function u = LaxFridrichs(a,dt,n,x1,x2,m)
format long;
h = (x2-x1)/(n-1);
for j=1:(n+2*m)
u0(j) =U(x1+(j-m-1)*h);
end
u1 = u0;
for k=1:m
for i=k+1:n+2*m-k
u1(i) = -(dt/h)*a*(u0(i+1)-u0(i-1))/2+(u0(i+1)+u0(i-1))/2;
end
u0 = u1;
end
x=0.01:0.01:n/100;
u = u1((m+1):(m+n));
plot(x,u,'r');
axis([0 1 -0.5 1.5]);
hold on
y=1.*(x<=0.5)+0.*(x>0.5);
plot(x,y,'c')
title('Lax-Fridrichs')
format short;
function ux =U(x)
format long;
if x<=0
ux=1;
else
ux=0;
end
>> u = LaxFridrichs(1,0.005,101,0,1,100)
运行结果
1 / 5
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