| Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions |
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| 作者姓名： | Jianming Liu |
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| 作者单位： | Jianming Liu (Department of Mathematics，Xuzhou Normal University，Xuzhou 221116，China Zhizhong Sun (Department of Mathematics，Southeast University，Nanjing 210096，China |
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| 基金项目： | 国家自然科学基金
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Foundation of Research Startup of Xuzhou Normal University
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国家自然科学基金 |
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| 摘 要： | 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 L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.
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Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions |
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| Jianming Liu.Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions[J].Numerical Mathematics A Journal of Chinese Universities English Series,2007,16(2):97-111. |
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| Authors: | Jianming Liu Zhizhong Sun |
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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 L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method. |
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| Keywords: | Reaction-diffusion nonlocal Robin type boundary finite difference solvability convergence |
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