Polynomial spline approach for solving second-order boundary-value problems with Neumann conditions |
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Authors: | Li-Bin LiuHuan-Wen Liu Yanping Chen |
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Affiliation: | a Department of Mathematics and Computer Science, Chizhou College, Chizhou, Anhui 247000, PR China b School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, PR China c School of Mathematical Sciences, South China Normal University, Guangzhou 510631, PR China |
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Abstract: | In this paper, a new difference scheme based on quartic splines is derived for solving linear and nonlinear second-order ordinary differential equations subject to Neumann-type boundary conditions. The scheme can achieve sixth order accuracy at the interior nodal points and fourth order accuracy at and near the boundary, which is superior to the well-known Numerov’s scheme with the accuracy being fourth order. Convergence analysis of the present method for linear cases is discussed. Finally, numerical results for both linear and nonlinear cases are given to illustrate the efficiency of our method. |
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Keywords: | Second-order boundary-value problem Neumann-type boundary condition Quartic spline Difference scheme High accuracy |
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