A New Family of High-Order Difference Schemes for the Solution of Second Order Boundary Value Problems

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BISHEH NIASAR MORTEZA; SAADATMANDI ABBAS; AKRAMI ARANI MOSTAFA

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Journal Paper

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Journal: Iranian Journal of Mathematical Chemistry Year:2018 | Volume:9 | Issue:3 Page(s): 187-199

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Title

A New Family of High-Order Difference Schemes for the Solution of Second Order Boundary Value Problems

Author(s)

BISHEH NIASAR MORTEZA | SAADATMANDI ABBAS | AKRAMI ARANI MOSTAFA | Issue Writer Certificate

Keywords

Boundary value problemsQ1

Finite difference methodsQ1

Bratu’s problemQ1

Troesch’s problemQ1

High accuracyQ1

Abstract

Many problems in chemistry, nanotechnology, biology, natural science, chemical physics and engineering are modeled by two point Boundary value problems. In general, analytical solution of these problems does not exist. In this paper, we propose a new class of high-order accurate methods for solving special second order nonlinear two point Boundary value problems. Local truncation errors of these methods are discussed. To illustrate the potential of the new methods, we apply them for solving some well-known problems, including Troesch’ s problem, Bratu’ s problem and certain singularly perturbed problem. Bratu’ s and Troech’ s problems, may be used to model some chemical reactiondiffusion and heat transfer processes. We also compare the results of this work with some existing results in the literature and show that the new methods are efficient and applicable.

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APA: Copy

BISHEH NIASAR, MORTEZA, SAADATMANDI, ABBAS, & AKRAMI ARANI, MOSTAFA. (2018). A New Family of High-Order Difference Schemes for the Solution of Second Order Boundary Value Problems. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 9(3 ), 187-199. SID. https://sid.ir/paper/205500/en

Vancouver: Copy

BISHEH NIASAR MORTEZA, SAADATMANDI ABBAS, AKRAMI ARANI MOSTAFA. A New Family of High-Order Difference Schemes for the Solution of Second Order Boundary Value Problems. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY[Internet]. 2018;9(3 ):187-199. Available from: https://sid.ir/paper/205500/en

IEEE: Copy

MORTEZA BISHEH NIASAR, ABBAS SAADATMANDI, and MOSTAFA AKRAMI ARANI, “A New Family of High-Order Difference Schemes for the Solution of Second Order Boundary Value Problems,” IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, vol. 9, no. 3 , pp. 187–199, 2018, [Online]. Available: https://sid.ir/paper/205500/en

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