Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions |
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Authors: | S Carl V Lakshmikantham |
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Institution: | a Fachbereich Mathematik und Informatik, Institut für Analysis, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany b Department of Mathematical Sciences, Florida Institute of Technology, 150 West University Boulevard, Melbourne, FL 32901-6988, USA |
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Abstract: | In this paper we consider an initial boundary value problem for a reaction-diffusion equation under nonlinear and nonlocal Robin type boundary condition. Assuming the existence of an ordered pair of upper and lower solutions we establish a generalized quasilinearization method for the problem under consideration whose characteristic feature consists in the construction of monotone sequences converging to the unique solution within the interval of upper and lower solutions, and whose convergence rate is quadratic. Thus this method provides an efficient iteration technique that produces not only improved approximations due to the monotonicity of its iterates, but yields also a measure of the convergence rate. |
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Keywords: | Generalized quasilinearization Reaction-diffusion equation Nonlinear and nonlocal boundary conditions Upper and lower solutions Quadratic convergence |
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