ecd_wave.m

偏微分方程matlab m文件

function [u,x,t] = ECD_Wave(A,xf,T,it0,i1t0,bx0,bxf,M,N)
%解方程a u_xx = u_tt for 0<=x<=xf, 0<=t<=T
% 初始条件: u(x,0) = it0(x), u_t(x,0) = i1t0(x)
% 边界条件: u(0,t)= bx0(t), u(xf,t) = bxf(t)
% M ：沿x轴的等分段数
% N ：沿y轴的等分段数
dx = xf/M; x = [0:M]'*dx;
dt = T/N; t = [0:N]*dt;
for i = 1:M + 1
    u(i,1) = it0(x(i)); 
end
for k = 1:N + 1
    u([1 M + 1],k) = [bx0(t(k)); bxf(t(k))];
end
r = A*(dt/dx)^ 2; r1 = r/2; r2 = 2*(1 - r);
u(2:M,2) = r1*u(1:M - 1,1) + (1 - r)*u(2:M,1) + r1*u(3:M + 1,1) + dt*i1t0(x(2:M)); %(11.3.4)
for k = 3:N + 1
    u(2:M,k) = r*u(1:M - 1,k - 1) + r2*u(2:M,k-1) + r*u(3:M + 1,k - 1)- u(2:M,k - 2); %(11.3.3)
end
u=u';