Solving Nonlinear PDEs in MATLAB: FDM or FEM Method? | Code Included

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    Matlab Nonlinear Pde
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SUMMARY

The discussion focuses on solving the nonlinear partial differential equation (PDE) given by u_{tt}=12{u_x}^2+12u_{xx}+{u_x}^4+6u_{xx}{u_x}^2+4u_{xxx}u_x+3{u_{xx}}^2+u_{xxxx} using MATLAB. Participants recommend exploring both the Finite Difference Method (FDM) and the Finite Element Method (FEM) for this purpose. The consensus is that MATLAB is capable of handling such PDEs, and users are encouraged to seek out existing code examples for adaptation to their specific problem.

PREREQUISITES
  • Understanding of nonlinear partial differential equations (PDEs)
  • Familiarity with MATLAB programming
  • Knowledge of Finite Difference Method (FDM)
  • Knowledge of Finite Element Method (FEM)
NEXT STEPS
  • Research MATLAB PDE Toolbox for built-in functions
  • Learn about implementing Finite Difference Method (FDM) in MATLAB
  • Explore Finite Element Method (FEM) applications in MATLAB
  • Find and modify existing MATLAB code for nonlinear PDEs
USEFUL FOR

Researchers, engineers, and students working on numerical methods for solving nonlinear PDEs, particularly those using MATLAB for simulations and modeling.

physgeekgeek
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I have the following equation to solve:

u_{tt}=12{u_x}^2+12u_{xx}+{u_x}^4+6u_{xx}{u_x}^2+4u_{xxx}u_x+3{u_{xx}}^2+u_{xxxx}

I have been told to look into FDM or FEM. My question, is it possible to code something in MATLAB to solve this and if so what is the best method to use and how do I do it? It would also be useful if there is some code already that I can change to fit the problem.

Cheers
 
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I am looking for solution u(x,t) btw
 

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