[anon_o]

Dear friends,
How can I write a program code (Fortran .f90) that solves square wave with lax wendroff method?
Thank you very much.
Best,
Armin😉

[FMDenaro]

This is a homework you can find developed in many textbooks...

[anon_o]

Originally Posted by FMDenaro

This is a homework you can find developed in many textbooks...

Could not find it or a sample of it in lax wendroff. That is why I asked it here.

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[FMDenaro]

Originally Posted by Arminsamadi

Could not find it or a sample of it in lax wendroff. That is why I asked it here.

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http://mathcenter.hust.edu.cn/Upload...98740d59f8.pdf

[selig5576]

This is a very straight forward problem and should take about 5 minutes given a the Lax-Wendroff article on wikipedia.

nx = 51;
x = zeros(nx,1);
u = zeros(nx,1);
a = 0.5
unew = zeros(nx,1)
dx = 300/nx;


for i=1:nx
x(i) = (i-1)*dx
end

for i=1:nx
if (x(i) > 0 && x(i) <= 50)
u(i) = 0;
else if (x(i) > 50 && x(i) <= 100)
u(i) = 3;
else if (x(i) > 100 && x(i) <= 300)
u(i) = 0
end

t = 0.0
while (t < tMax)
for i=2:nx-1
unew(i) = u(i) - (dt/2*dx)*a*(u(i+1) - u(i-1)) + (dt^2)/(2*dx.^2)*a^2*(u(i+1) - 2*u(i) + u(i-1))
end

u = unew
t = t + dt
end

plot(x,u,'-o')

The code I wrote for you is in Matlab, but can be ported to Fortran in a matter of minutes. You will need to satisfy boundary conditions. As a side note, you can also reformulate the Lax-Wendroff method as a 2 step method which you will need to do if you were to solve a nonlinear problem.

[anon_o]

Originally Posted by selig5576

This is a very straight forward problem and should take about 5 minutes given a the Lax-Wendroff article on wikipedia.

nx = 51;
x = zeros(nx,1);
u = zeros(nx,1);
a = 0.5
unew = zeros(nx,1)
dx = 300/nx;


for i=1:nx
x(i) = (i-1)*dx
end

for i=1:nx
if (x(i) > 0 && x(i) <= 50)
u(i) = 0;
else if (x(i) > 50 && x(i) <= 100)
u(i) = 3;
else if (x(i) > 100 && x(i) <= 300)
u(i) = 0
end

t = 0.0
while (t < tMax)
for i=2:nx-1
unew(i) = u(i) - (dt/2*dx)*a*(u(i+1) - u(i-1)) + (dt^2)/(2*dx.^2)*a^2*(u(i+1) - 2*u(i) + u(i-1))
end

u = unew
t = t + dt
end

plot(x,u,'-o')

The code I wrote for you is in Matlab, but can be ported to Fortran in a matter of minutes. You will need to satisfy boundary conditions. As a side note, you can also reformulate the Lax-Wendroff method as a 2 step method which you will need to do if you were to solve a nonlinear problem.

Your code was not working, I wrote this:
CLC

CLEAR ALL

L=300;

DT=2;

DX=2;

A=0.05;

C=A*DT/DX;

M=L/DX;

T=1000;

N=ROUND(T/DT);

E=0.01

FOR I=1:M

IF (I
-.5)*DX<=50
U(I,1)=0;

ELSE IF (I-.5)*DX<=110

U(I,1)=3;

ELSE

U(I,1)=0;

END

END

END

FOR J=2:N

FOR I=2:M-1

U(I,J)=U(I,J-1)-.5*C*(U(I+1,J-1)-U(I-1,J-1))+(E+.5*C^2)*(U(I+1,J-1)-2*U(I,J-1)+U(I-1,J-1));

END

END

FOR I=1:M

X(I)=(I-.5)*DX;

END

PLOT(X,U(:,N))

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[FMDenaro]

I suggest to see the implementation of the L-W scheme both in non-conservative and conservative form. See the book of Leveque.

[selig5576]

A. It is helpful if you post your code around code tags.
B. You need to be specific on whats not working.
C. I don't see any boundary conditions. Your problem is not posed well with only an initial condition given you have spatial and temporal variables in your problem.

You are looping through the interior domain, but you are not specifying what is happening on the boundary. For example Dirichlet boundary conditions will mean unew(1) = ua, unew(nx) = ub. ua and ub are values that the equation attains at the boundary of your domain. If you have periodic boundary conditions you will have unew(1) = unew(nx).