How to solve differential equation

Hello,

I have the following equations as seen below, and I need to get out p(x) and t(x). I understand that maybe Runge Kutta method should be used, but I do not se how I can solve it. I write "integrate" to show how the equation looks, not that I believe that matlab works that way.

Constants: Er, Es, pi, xa, xd, t1, R, my, vs.

b(x) = -(2/(pi*Er))*integrate[(p(s)*ln(abs((s+xa)/s-x))]ds; % integrate from -xa to xd

t(x) = t1 - (xa^2-x^2)/R + 2*b(x);

q(x) = my*p(x);

dp/dx = -(Es/t(x))*dt/dx+(vs/(1-vs))*2*q(x)/t(x);

It would be amazing if anyone could help me!

Best regards

Christopher

[Torsten]

... and the differential equation for p is to be integrated from -xa to xd ?

... and you are sure that the integral in the expression for b(x) is to be taken between -xa and xd, not between -xa and x ?

Best wishes

Torsten.

[Christopher Fallqvist]

Yes, you are right Torsten. Thanks.

Christopher

[Torsten]

So p is to be integrated between -xa and xd and the integral in the expression for b(x) is to be taken between -xa and xd, too ?

Best wishes

Torsten.

[Christopher Fallqvist]

Sorry for misleading you with my last answer: I ment between -xa and x.

Best regards

Christopher

Answer 1

[Torsten]

Choose a grid of stepsize deltax: -xa=x0<x1<x2<...<x_n=xb with x_(i+1)-x_i=deltax.

I suggest you use backward differencing for dp/dx and the trapezoidal rule for the integral.

You'll arrive at n nonlinear equations with unknowns p(x1),...,p(x_n).

The equations can be solved one after the other (sequentially) using MATLAB's "fzero".

Best wishes

Torsten.

[Christopher Fallqvist]

Thank you!

I will try this and see if I solve the problem. Thanks again.

Best regards

Christopher