MATLAB has really good tutorials aavilable on PDE solvers and various applications:

https://uk.mathworks.com/products/pde.html

https://uk.mathworks.com/help/pde/getting-started-with-partial-differential-equation-toolbox.html

I recommend going through these as starters to see what can you achieve with MATLAB, then try to implement your specific equations.

Best regards

David

In Matlab you have also the pdetool but honestly I think you can solve directly the equations, they appears in the form of ODE-like.

Start using simple first order accuracy to have a reference solution, then you can use higher order schemes.

Keep in mind that there are few cases in which you can calculate exact solutions of initial and boundary value problems. In most cases we are forced to calculate approximate solutions in discrete domains, that is, with a finite number of points and not in the continuous domain, which requires replacing the problem in PDE with a problem expressed through relationships based on finite differences, finite elements, finite volumes and others. You can use Newton Raphson's method to solve this approximate system in the finite set of points. Not the original initial and boundary value problem .

Keep in mind that there are few cases in which you can calculate exact solutions of initial and boundary value problems.

In most cases we are forced to calculate approximate solutions in discrete domains, that is, with a finite number of points and not in the continuous domain, which requires replacing the problem in PDE with a problem expressed through relationships based on finite differences, finite elements, finite volumes and others.

You can use Newton Raphson's method to solve this approximate system in the finite set of points. Not the original initial and boundary value problem .

Keep in mind that there are few cases in which you can calculate exact solutions of initial and boundary value problems.

In most cases we are forced to calculate approximate solutions in discrete domains, that is, with a finite number of points and not in the continuous domain, which requires replacing the problem in PDE with a problem expressed through relationships based on finite differences, finite elements, finite volumes and others.

• Keep in mind that there are few cases in which you can calculate exact solutions of initial and boundary value problems.
• In most cases we are forced to calculate approximate solutions in discrete domains, that is, with a finite number of points and not in the continuous domain, which requires replacing the problem in PDE with a problem expressed through relationships based on finite differences, finite elements, finite volumes and others.
• You can apply Newton Raphson's method to solve this approximate system in the finite set of points. Not the original initial and boundary value problem .

Keep in mind that there are few cases in which you can calculate exact solutions of initial and boundary value problems.

In most cases we are forced to calculate approximate solutions in discrete domains, that is, with a finite number of points and not in the continuous domain, which requires replacing the problem in PDE with a problem expressed through relationships based on finite differences, finite elements, finite volumes and others.

You can apply Newton Raphson's method to solve this approximate system in the finite set of points, not the original initial and boundary value problem.

Evalúate results

Dear Kamchau:

You can use the function "fsolve" to solve non linear system equations. It's easy to apply. You can explore the documentation and examples related in Matlab.

Goog luck!

Thank you for all of your comment. I am trying to program it now which is harder than I thought. My plan is to use fsolve to solve it first, once it success, i will use it on Newton-raphson method.

Currently I am trying to use fsolve at the moment, however, the equations are represent in matrix form, it seems not really welcome by using fsolve.

Anyone have experience with using fsolve to work in the matrix format?

I recomend to you create a function in MatLab that include your PDE system in finite differences ( resulting a non linear system equations, eg. yourfun).

Then, in the main script, you can apply fsolve tool to call 'yourfun' !. It's important you note that in fsolve options, you can employ Newton's methods and similars, like Levenberg-Marquardt.

Good luck!

I recommend you try mathwork.com. It will guide you a lot on this problem. Best of luck

Thank you everyone! I have finally solved it out!

Best wish to all of you!