Abstract
Non-linear diffusion equations with numerical stability problems are common in many branches of science. An example is the k-diffusion parametrization for vertical turbulent mixing in atmospheric models that creates a system of non-linear diffusion equations with stability problems. In this paper a new algorithm to solve the one-dimensional diffusion equation is presented. This method, which is stable by design, is quite general and can be used in other partial differential equations. Results with the new scheme compare well with analytical solutions, and a study with a system of two non-linear diffusion equations shows that the new method is more stable than more traditional schemes.
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