ANALYSIS OF STABILITY AND ERROR ESTIMATES FOR THREE METHODS APPROXIMATING A NONLINEAR REACTION-DIFFUSION EQUATION

Costică Moroşanu; Silviu Pavăl; Cătălin Trenchea

doi:10.11948/2017001

2017 Volume 7 Issue 1

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Costică Moroşanu, Silviu Pavăl, Cătălin Trenchea. ANALYSIS OF STABILITY AND ERROR ESTIMATES FOR THREE METHODS APPROXIMATING A NONLINEAR REACTION-DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 1-19. doi: 10.11948/2017001

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Costică Moroşanu, Silviu Pavăl, Cătălin Trenchea. ANALYSIS OF STABILITY AND ERROR ESTIMATES FOR THREE METHODS APPROXIMATING A NONLINEAR REACTION-DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2017, 7(1): 1-19. doi: 10.11948/2017001

ANALYSIS OF STABILITY AND ERROR ESTIMATES FOR THREE METHODS APPROXIMATING A NONLINEAR REACTION-DIFFUSION EQUATION

1 Department of Mathematics, University of Iasi, bd. Carol I, Iasi, 700506, Romania;
2 Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

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Abstract

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^∞ 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.
- Nonlinear PDE of parabolic type /
- finite difference methods /
- Newton method /
- fractional steps method /
- stability and convergence of numerical methods
MSC: 35K55;65M06;65M12;65Y20;80A22

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