Lax wendroff Two-step method

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kyle lyth
kyle lyth 2012-2-22
hi i am trying to program a generalised lax wendroff two step method to solve the general equation
du/dt + df(u)/dx = 0
the code i have come up with is as shown below (sorry im not sure how to make it look more tidy)
i belive im doing something wrong in the first step with no F function included, however when i place this in or try to i get a graph that can't possibly be correct
thanks for any help kyle
function compare close all;clc;clear all
%intial values
ntime = 1000000; dt=0.00040; nx=100; time = 0; a=1;output=0.4;
%step size calculation
dx= (1/nx);
%create size of u_int vector
u_int = zeros(nx,2);
%create little u_int vector for the initial values of height begining and end depending which value of A is used
u_int(nx,2) = 1;
u_int(1,1) = 1;
%loop for the two directions needed
for vec = 1:2
% %lax_wendroff
[U] = lax_wendroff_2(nx,a,output, dt, ntime, time,u_int, vec,dx);
figure(vec)
plot(U(:,vec),'r*');grid on;legend('centered');
hold on
end
end
function [U] = lax_wendroff_2(nx,a,output, dt, ntime, time,u_int, vec,dx);
%compute original size matracies
U=zeros(nx,1);
update = U ;
F = U;
if vec == 1;
U(1,vec)=u_int(1,vec);
A=a;
else
U(nx,vec)=u_int(nx,vec);
A=-a;
end
for p = 1:ntime;
if(time + dt>output); dt=output-time;
end
coeff=dt/dx;
%calculate interim steps
for i = 1:(nx-1)
F(i+1,vec)= ((U(i,vec)+U(i+1,vec))/2) - ((A*coeff)*((U(i+1,vec) - U(i,vec))));
end
for i = 2:(nx-1)
update(i,vec) = U(i,vec) - coeff*A*(F(i+1,vec) - F(i,vec));
end
for i = 2:(nx-1)
U(i,vec) = update(i,vec);
end
time = time + dt;
if time==output
break
end
end end

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