Help How to solve a set of 12 partial differential equations with 8 variables.

[tiantsai]

Hi, I am a master student comes from USM in Malaysia. My main focus is on monopole instanton solution in static form which did not include time, i using the Lagrangian to generate out the 12 set equations of motion with 8 variables, the software that i use is Matlab with Optimization toolbox- the algorithm that i use inside the package is trusted reflective region and the numerical method that i used is finite difference method. However, it did not converge. I have tried to reproduce the Jutta Kunz paper-monopoles solution with 6 set of partial differential equation with 6 variables and its work well and i can get the Higgs field of monopole successfully. The varibale is in r and theta form which means as A(r,theta). So any suggestion for using Matlab to solve the 12 set equations of motion (PDE form) with 8 variables.

 

[gtoguy97]

It sounds like you have a very challenging problem. It is difficult to give specific advice without knowing the exact equations and variables that you are working with, but here are some general tips that may help:1. Make sure you are using the right numerical methods for your problem. Depending on the form of the equations, different techniques may work better than others. For instance, if your equations are nonlinear, then a finite difference method may be more appropriate than a finite element method.2. Use an adaptive approach if possible. This means that you can adjust the mesh size or the number of points used in the solution as it progresses, which can help to improve the accuracy and speed of convergence.3. Consider using a different software package, such as COMSOL or ANSYS, which have more sophisticated tools for solving PDEs.4. Look for specific methods designed for solving your type of equations. For example, if your equations are of the form of an elliptic partial differential equation (PDE), then there may be specific algorithms designed to solve this type of equation quickly and accurately.I hope these tips are helpful! Good luck!