Coupled system of 1st order PDEs

Thread starter hunt_mat
Start date Jun 8, 2011
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Coupled Pdes System

Jun 8, 2011

hunt_mat

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I have the following system of first order PDEs
 \begin{array}{rcl} \frac{\partial v}{\partial t}+v\frac{\partial v}{\partial x} & = & -\varepsilon\gamma^{-3}(v)E \\ \frac{\partial n}{\partial t}+\frac{\partial}{\partial x}(nv) & = & 0 \\ \frac{\partial E}{\partial t}+E & = & nv \end{array} 
With inital conditions v(t,0)=\beta_{0},n(0,x)=1,E(x/\beta_{0},x)=0. Now it is possible to solve for E explicitly to obtain:
 E(t,x)=\int_{\frac{x}{\beta_{0}}}^{t}e^{s-t}n(s,x)v(s,x)ds 
Now I have decided to solve this system numerically using a predictor corrector method for v and n and the solution above to find E. Now I have got the predictor-corrector to work (such that it gives no errors when I run it) but I am having a little trouble coding up the integral for E, can anyone suggest something? I am working in MATLAB.

Cheers

Mat

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