Having a problem with solving a second order ODE equation using Matlab

[kubekas]

I am having a problem coding a Matlab code that solves a second ODE equation which I give below:

x^3*(1-2*x*M)d^2J(x)/dx^2+2*(2*x^2+i*nu*x-7*x^3*M)*dJ(x)/dx
-2*(2*x+8*M*x^2+i*nu)*J(x)=0.

where

M = 1 (Mass of a black hole),
nu = 0.74734+0.17792*i,
J is a function of x,
i represents a complex number.

This equation is very complex to solve. Fistly I tried the Matlab shooting
method and it did not work because this equation is singular at the boundries i.e
0 and 1. Now I am trying to solve it using Matlab Finite Difference Method. I must point out that this problem has no analytic solution and we hope that it can be solved numerically.

Can anyone out there help me with this problem.
Thanks
Amos

 

[Aaron Bex]

The finite difference method is most likely the best option for solving this equation. To use the finite difference method, you need to discretize the equation by replacing the derivatives with finite differences. This is done by approximating the derivatives using values of the function at nearby points. The finite difference weights will depend on the number of points used and the spacing between the points. Once the equation is discretized, it can be solved using linear algebra methods such as a matrix inversion. For more information on how to implement the finite difference method, please refer to the documentation provided by Matlab.

 

[tacman]

Hello Amos,

Thank you for reaching out for help with your problem. Solving second order ODE equations using Matlab can be tricky, especially when they involve complex numbers and have no analytical solution. However, there are a few steps you can follow to help you code a successful solution using Matlab.

Firstly, make sure you have a good understanding of the problem and the equation you are trying to solve. This will help you in choosing the appropriate method and approach for solving it. In this case, it seems like the Finite Difference Method would be a good approach to use.

Next, try breaking down the equation into smaller parts and solving them separately. This will make the coding process easier and more manageable. You can also try using symbolic variables in Matlab to represent the complex parts of the equation.

Another helpful tip is to use built-in Matlab functions and tools, such as the "ode45" function or the "dsolve" command, to help solve the equation. These functions are specifically designed for solving ODE equations and can save you a lot of time and effort.

Lastly, don't be afraid to reach out to online forums or communities for help. There are many experienced Matlab users who are willing to assist and provide guidance on coding solutions for complex equations.

I hope these tips will help you in successfully solving your equation using Matlab. Good luck!