Volume 16, Issue 2
Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions

J. M. Liu & Z. Z. Sun

DOI:

Numer. Math. J. Chinese Univ. (English Ser.)(English Ser.) 16 (2007), pp. 97-111

Published online: 2007-05

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  • Abstract

In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete $L_2$-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.

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@Article{NM-16-97, author = { J. M. Liu and Z. Z. Sun}, title = {Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions}, journal = {Numerical Mathematics, a Journal of Chinese Universities}, year = {2007}, volume = {16}, number = {2}, pages = {97--111}, abstract = { In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete $L_2$-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nm/8049.html} }
TY - JOUR T1 - Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions AU - J. M. Liu & Z. Z. Sun JO - Numerical Mathematics, a Journal of Chinese Universities VL - 2 SP - 97 EP - 111 PY - 2007 DA - 2007/05 SN - 16 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/nm/8049.html KW - AB - In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete $L_2$-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.
J. M. Liu & Z. Z. Sun. (1970). Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions. Numerical Mathematics, a Journal of Chinese Universities. 16 (2). 97-111. doi:
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