| Volume 7, Number 1, 2017, Pages 1-19 DOI：10.11948/2017001 |
| Analysis of stability and error estimates for three methods approximating a nonlinear reaction-diffusion equation |
| Costic\u a Moro\c sanu,Silviu Pav\u al,C\u at\u alin Trenchea |
| Keywords:Nonlinear PDE of parabolic type, finite difference methods, Newton method, fractional steps method, stability and convergence of numerical methods. |
| Abstract: |
| We present the error analysis of three time-stepping schemes used in the discretization of a nonlinear reaction-diffusion equation with Neumann boundary conditions, relevant in phase transition. We prove $L^\infty$ stability by maximum principle arguments, and derive error estimates using energy methods for the implicit Euler, and two implicit-explicit approaches, a linearized scheme and a fractional step method. A numerical experiment validates the theoretical results, comparing the accuracy of the methods. |
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