How to change initial condition?

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sing lai 2014-2-25

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https://ww2.mathworks.cn/matlabcentral/answers/119035-how-to-change-initial-condition

编辑： sing lai 2014-2-25

 ffunction [u,x,t] = wave(a,xf,T,it0,i1t0,bx0,bxf,M,N)
%solve a u_xx = u_tt for 0<=x<=xf, 0<=t<=T
% Initial Condition: u(x,0) = it0(x), u_t(x,0) = i1t0(x)
% Boundary Condition: u(0,t)= bx0(t), u(xf,t) = bxf(t)
% M = # of subintervals along x axis
% N = # of subintervals along t axis
%solve_wave
a = 1;
it0 = inline('x.*(1-x)','x'); i1t0 = inline('0'); %initial condition
bx0 = inline('0'); bxf = inline('0'); %boundary condition
xf = 1; M = 10; T = 2; N = 10;
dx = xf/M; x = [0:M]'*dx;  %space step size
dt = T/N; t = [0:N]*dt;    %time step size
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)); 
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); 
end
figure(1), clf
mesh(t,x,u)
figure(2), clf
for n = 1:N %dynamic picture
plot(x,u(:,n)), axis([0 xf -0.3 0.3]), pause(0.2)
end