Suggestions to numerically solve the following system of differential equations?

Kareemulla Dudekula @Kareemulla-Dudekula

10 October 2020 4 10K Report

Hello All,

I am a novice to numerical methods. I am trying to numerically solve the following two coupled equations using Matlab; any suggestions are greatly appreciated.

Flux balance in spherical coordinates:

d/dr(r^2*N(r)) = r^2*[Ko*Exp(-E/R/T(r))*(Vmax - V(r))].....................(1)

The term in [ ] is a source term.

N is zero at r = 0 (symmetric boundary condition);

Flux, N, is here is convective in nature and is due to pressure gradient as given below.

N = (K/u)*(P(r)/r/T(r))*dP(r)/dr..................................................(2)

P is Ps at r = R (surface).

I have already worked out the T(r) and V(r) profiles separately.

Thanks!

Zoleikha Soori

You can use the Maple software and solve this equation with "solve" code. For more details, I suggest the "help" section.

Muhammad Ali

Have a look at via MATLAB :: https://au.mathworks.com/help/matlab/math/partial-differential-equations.html

https://au.mathworks.com/help/matlab/math/solve-angio-pde-system.html

ode45 : : https://au.mathworks.com/help/matlab/ref/ode45.html

Graham W Griffiths

Dear Kareemulla Dudekula,

You do seem to understand the problem well and therefore are on track to solving this system of coupled PDEs. From your question, it seems that you need some help in obtaining the numerical solution.

Please download the Matlab code from

www.pdecomp.net

associated with the book: "A Compendium of Partial Differential Equation Models". This code may give you some ideas for going forward. The code for chapter 13 should be useful as it solves coupled reaction PDEs in cylindrical coordinates for composition and temperature. It should provide you with a pointer with regard to handling coupled Rx PDEs and, in particular, the radial coordinate part of your problem in Matlab.

I hope this provides some help.

Kind regards,

Graham W Griffiths

Alexander Bortsov

For the numerical solution of a system of five equations use differential equations. The first partial differential equation is the most difficult to represent.Initially, the principles for deriving the difference equation for your differential equations can be found at the link.Different approximation schemes and programs are presented here.

https://hplgit.github.io/prog4comp/doc/pub/p4c-sphinx-Python/._pylight005.html

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