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Title: High accuracy variable mesh method for nonlinear two-point boundary value problems in divergence form
Authors: Jain, Manoj Kumar
Sharma S.
Mohanty R.K.
Published in: Applied Mathematics and Computation
Abstract: In this article, using three grid points, we discuss variable mesh method of order three for the numerical solution of nonlinear two-point boundary value problems: (p(x)y')'=f(x,y),y(0)=A,y(1)=B. We first establish an identity from which general three-point finite difference approximation of various order can be obtained. We obtain a family of third order discretization using variable mesh for the differential equations. We select the free parameter available in this discretization which leads to the simplest third order method. Numerical results are provided to illustrate the proposed method and their convergence. © 2015 Elsevier Inc.
Citation: Applied Mathematics and Computation (2016), 273(): 885-896
Issue Date: 2016
Publisher: Elsevier Inc.
Keywords: Divergence form
Finite difference method
Nonlinear equation
Two-point boundary value problems
Variable mesh
ISSN: 963003
Author Scopus IDs: 57225721930
Author Affiliations: Jain, M.K., Department of Mathematics, Indian Institute of Technology, Hauz KhasNew Delhi 110016, India, 4076, C/4, VasantKunj, New Delhi 110070, India
Sharma, S., Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110007, India
Mohanty, R.K., Department of Applied Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi 110021, India
Funding Details: The authors thank the reviewers for their valuable suggestions, which substantially improved the standard of the paper. This work is supported by “Council of Scientific and Industrial Research (CSIR), New Delhi, India” under the grant no. 09/045(1161)/2012-EMR-I.
Corresponding Author: Mohanty, R.K.; Department of Applied Mathematics, South Asian University, Akbar Bhawan, India
Appears in Collections:Journal Publications [HY]

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