Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients

Abstract EN

Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting.

Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values.

A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions.

The superiority of the method is also demonstrated by showing comparison with Newton's method.