RK method for heat equation with dependent variables

In summary, the speaker was struggling to solve an equation without removing the k(y) term and was planning to use a numerical solution method. However, they were unsure if removing the k(y) term was the correct approach. They later found a solution by using a different substitution method.
  • #1
maistral
240
17
Hello.

How do I solve this equation without killing the k(y) term:
1.png


I managed to derive an analytical solution for this one. I intend to run the numerical solution via Runge-Kutta but I can't stop myself from killing the k(y) term. I'm starting to think I'm doing something wrong... It goes something like this:

22.png


Even if I try and keep the k(y) term until I derive the systems of equations required to run Runge-Kutta, the integrator would then numerically kill it anyway. What should I do?
Any help please?
 
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  • #2
Nevermind. Solved it by using a proper substitution.
 

1. What is the RK method for heat equation with dependent variables?

The RK method, also known as the Runge-Kutta method, is a numerical method used to solve differential equations, such as the heat equation. It is an iterative process that uses a series of steps to approximate the solution to the equation.

2. How does the RK method work for heat equation with dependent variables?

The RK method works by breaking down the differential equation into smaller steps, and using a weighted average of the slopes at each step to approximate the solution. It is a widely used method due to its simplicity and accuracy.

3. What are the advantages of using the RK method for heat equation with dependent variables?

One of the main advantages of the RK method is its flexibility. It can handle a wide range of differential equations, including the heat equation with dependent variables. It also provides a trade-off between accuracy and computational cost, making it a popular choice for numerical solutions.

4. Are there any limitations to using the RK method for heat equation with dependent variables?

One limitation of the RK method is that it can be computationally expensive for systems with many dependent variables. It also requires a certain level of expertise to determine the appropriate step size and number of steps for accurate results.

5. How can I implement the RK method for heat equation with dependent variables in my research?

There are many resources available online that provide step-by-step guides on implementing the RK method for various differential equations, including the heat equation with dependent variables. You can also consult with a numerical analysis expert for guidance and assistance in implementing the method in your research.

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