Graduate RK method for heat equation with dependent variables

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The discussion focuses on solving a heat equation with a dependent variable k(y) without eliminating it during the numerical solution process. The user initially struggles to maintain the k(y) term while applying the Runge-Kutta method, leading to concerns about its numerical stability. After attempting various approaches, including deriving systems of equations, the user finds that the integrator still removes the k(y) term. Ultimately, the issue is resolved through a proper substitution technique. The conversation highlights the challenges of incorporating variable coefficients in numerical methods for differential equations.
maistral
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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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Nevermind. Solved it by using a proper substitution.
 

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