A Comparative Study of the Numerical Approximations of the Quenching Time for a Nonlinear Reaction-Diffusion Equation

Abstract

In this paper, we study the numerical methods for solving a nonlinear reaction-diffusion model for the polarization phenomena in ionic conductors. In particular, we propose three types of numerical methods, including the finite difference, cubic B-spline collocation, and local discontinuous Galerkin method, to approximate the quenching time of the model. We prove the conservation properties for all three numerical methods and compare their numerical performance.

Keywords

• Cubic B-spline collocation method
• Finite difference method
• Local discontinuous Galerkin method
• Reaction-diffusion equation
• Quenching time

References

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