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New Finite Difference Schemes On Reaction-Diffusion Equations

Posted on:2008-09-18Degree:MasterType:Thesis
Country:ChinaCandidate:W J ZhaoFull Text:PDF
GTID:2120360212990882Subject:Applied Mathematics
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This paper discussed two kind of new difference algorithms for non-linear parabolic equations initial-boundary value problems as follows:It is a reaction-diffusion type model for the propagate density of bacterial cells and the concentration of nutrient. The essential assumption is that there exist two type bacterial cells.Take Fisher equation for example,the first method is a modification of Crank-Nicolson scheme,which is denoted by TGCN for short.We apply TGCN scheme to reaction-difiusion equations and compare to Crank-Nicolson scheme,the numerial result of TGCN scheme has higher precision, and make its coefficient matrix diagonally domainant.So the difference equation can be sloved directly.The second method is the improvement of Predictor-Corrector scheme, and denoted by CJPC for short. This method applies the traditional Predictor-Corrector(PC) scheme of quasilinear parabolic equation to reaction-diffusion equations, then modifies the nonlinear term of Corrector scheme.Generally speaking,the computation cost of PC scheme is not high, Predictor and Corrector difference equations are tri-diagonal equations. When given initial and boundary conditions,they can be solved by chasing method.Numerical experiment indicate that GJPC scheme has a good improvement on stability and computation precision. In conclusion,it is a good difference method.Two kind of differences algorithms discussed above have the practicability. The second method elicit us it is important to deal with nonlinear term in doing differences algorithm of nonlinear parabolic system.
Keywords/Search Tags:Reaction-diffusion equations, Crank-Nicolson scheme, Predictor-Corrector scheme, modified equation
PDF Full Text Request
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