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Asymptotic properties of a class of reaction-diffusion equation spectral method of solutions and error estimates prolonged

Author: CaoYang
Tutor: ZhangFaYong
School: Heilongjiang University
Course: Applied Mathematics
Keywords: Legendre pseudospectral method Error estimation on large time asymptotic stbility reaction-diffusion equation
CLC: O241.8
Type: Master's thesis
Year: 2006
Downloads: 34
Quote: 0
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Abstract


In the paper, a class of reaction-diffusion equation is considered.In the first part, first of all, we have a priori estimate for solution of the reaction-diffusion equation with initial condition and Dirichret boundary conditions. Then, we construct a semidiscrete Legendre pseudospectral scheme, and have a priori estimate for approximate solution. We discuss the asymptotic stability of approximate solution. At last, we get a error estimation on large time for solution of the semidiscrete system.In the second part, we construct a completely discrete Legendre pseu-dosepectral scheme. By using the same procedures as the discussion of the semidiscrete system, we get some results which are opposite to the results of semidiscrete system in the completely discrete system.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
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