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I have the following system of PDE's:

u_{t}= v_{x}

v_{t}= (-3)*u_{x}+ 4*v_{x},

with initial conditions u(x,0) = sin (x), v(x,0) = 0. I am only considering the region 0<x<2*pi and 0<t<4*pi. The solution is assumed to be periodic in space.

Using MATLAB, I want to discretize in space using a central difference quotient, and then apply the 4:th order Runge-Kutta method in time.

Being new to both numerical methods as well as MATLAB I have been unable to manage this task. I found this m-file for system of ODE's:

http://matlabdb.mathematik.uni-stuttgart.de/runge_kutta4.m?MP_ID=405" [Broken]

I tried modifying it to suit my purpose but it wouldn't work. Is there an easy way to modify it when I include the space discretization? Or does anyone have a better idea?

Thanks for taking a look.

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# 4:th order Runge-Kutta for system of PDE's

Can you offer guidance or do you also need help?

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