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

In summary, a nonlinear PDE is a mathematical equation that involves multiple variables and their partial derivatives, and is not easily solved by simple addition or subtraction. These equations are difficult to solve because they do not have a closed-form solution and often require numerical methods. MATLAB is a useful tool for solving tricky nonlinear PDEs due to its built-in functions and visualization capabilities. Nonlinear PDEs have various applications in different fields, but there are limitations to using MATLAB, such as the size and complexity of the problem and the accuracy of the numerical methods. Other software or techniques may be necessary to obtain a more precise solution in some cases.
  • #1
physgeekgeek
4
0
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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  • #2
I am looking for solution u(x,t) btw
 

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

1. What is a nonlinear partial differential equation (PDE)?

A nonlinear PDE is a mathematical equation that involves multiple variables and their partial derivatives, and where the relationship between these variables is not linear. This means that the solution to the equation cannot be easily determined by simply adding or subtracting the variables.

2. Why are nonlinear PDEs difficult to solve?

Nonlinear PDEs are difficult to solve because they do not have a simple, closed-form solution like linear PDEs. This means that numerical methods, such as using computers and algorithms, are often needed to approximate a solution.

3. How can MATLAB be used to solve tricky nonlinear PDEs?

MATLAB is a powerful tool for solving tricky nonlinear PDEs because it has built-in functions and algorithms specifically designed for solving these types of equations. Additionally, MATLAB allows for easy visualization of the solution, which can aid in understanding and analyzing the results.

4. What are some common applications of nonlinear PDEs?

Nonlinear PDEs have a wide range of applications in various fields, such as physics, engineering, and finance. They can be used to model complex systems and phenomena, such as fluid dynamics, heat transfer, and population dynamics.

5. Are there any limitations to using MATLAB for solving nonlinear PDEs?

While MATLAB is a powerful tool, it does have some limitations when it comes to solving tricky nonlinear PDEs. These limitations may include the size and complexity of the problem, as well as the accuracy and efficiency of the numerical methods used. In some cases, it may be necessary to use other software or techniques to obtain a more accurate solution.

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