Numerically solving 2 coupled PDEs

In summary, The conversation discusses the problem of solving a system of two coupled partial differential equations in MATLAB, with certain initial conditions and constraints. The speaker has attempted to use the function pdepe but encountered errors, and has also tried a numerical solving approach but received values outside of the expected range. They are seeking advice on how to address this issue and suggests checking the coefficients and the stability of the numerical method used.
  • #1
niha1794
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I want to solve a system of 2 coupled pde (in MATLAB) of the format:

c1*(df/dt)+c2*(df/dz)+c3*(f)+c4*(g)=0

(dg/dt)=c5*f+c6*g

with Initial conditions as
f(0,t)=1, g(z,0)=0 and f(z,0)=0

0<f,g,z,t<1

I tried using the MATLAB function pdepe to do this but got errors and if I go for numerical solving by finite difference method I get the value of f>1 which is not possible.

Please help me with this problem!
 
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  • #2
If you get values outside of the expected range you better check the values of the coefficients ##c_i## and the stability of the numerical method due to the choosen spatial and temporal steps ##\Delta z## and ##\Delta t##, respectively.
 
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1. What are coupled PDEs?

Coupled PDEs (partial differential equations) are a set of two or more equations that are connected through their variables. This means that the solutions of these equations are interdependent and affect each other.

2. How are coupled PDEs solved numerically?

Coupled PDEs can be solved numerically using various methods such as finite difference, finite element, or spectral methods. These methods involve discretizing the equations and solving them using numerical algorithms.

3. What are the challenges in numerically solving coupled PDEs?

Numerically solving coupled PDEs can be challenging due to the complexity of the equations, the need for high computational power, and the potential for numerical errors. Furthermore, the solutions may require a large number of grid points, making the calculations time-consuming.

4. What are some applications of numerically solving 2 coupled PDEs?

Numerical solutions of 2 coupled PDEs have a wide range of applications in engineering, physics, and other scientific fields. They are used to model and analyze various physical phenomena, such as heat transfer, fluid flow, and wave propagation. They are also used in designing and optimizing systems and processes.

5. Are there any software packages available for solving coupled PDEs?

Yes, there are various software packages available for numerically solving coupled PDEs, such as MATLAB, COMSOL, and ANSYS. These packages provide a user-friendly interface and a wide range of numerical methods for solving coupled PDEs. They are also equipped with visualization tools to help analyze and interpret the results.

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