Lax-wendroff.rar

clear; close all a = 0; b=1; tfinal = 1; m = 20; h = (b-a)/m; k = 0.01; t = 0; n = fix(tfinal/k); y1 = zeros(m+1,1); y2=y1; x=y1; for i=1:m+1, x(i) = a + (i-1)*h; y1(i) = uexact(t,x(i)); y2(i) = 0; end figure(1); plot(x,y1); hold t = 0; for j=1:n, y1(1)=bc(t); y2(1)=bc(t+k); y2(2:m) = 0.5*9*k^2/(h^2)*(y1(1:m-1)+y1(3:m+1)-2*y1(2:m)) - 0.5*3*k/h*(y1(3:m+1)-y1(1:m-1))+y1(2:m); i = m+1; y2(i) = 0.5*9*k^2/(h^2)*(y1(i-2)+y1(i)-2*y1(i-1)) - 3*k/h*(y1(i)-y1(i-1))+y1(i); t = t + k; y1 = y2; plot(x,y2); pause(0.005) end plot(x,y2,'o') u_e = zeros(m+1,1); % for i=1:m+1 % u_e(i) = uexact(t,x(i)); % end % for i=1:m+1 u_e(1:m+1) = uexact(t,x(1:m+1)); % end max(abs(u_e-y2)) figure(2); plot(x,y2,'o',x,u_e)