A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems

A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems

A family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed. The methods which can be applied in pr...

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Main Authors: F. F. Ngwane, S. N. Jator
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2015/343295
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spelling doaj-71a37f28efe845e2b2393952267d38bc2020-11-24T22:35:55ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/343295343295A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value ProblemsF. F. Ngwane0S. N. Jator1Department of Mathematics, USC Salkehatchie, Walterboro, SC 29488, USADepartment of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USAA family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed. The methods which can be applied in predictor-corrector form are implemented in block form as simultaneous numerical integrators over nonoverlapping intervals. Numerical results obtained using the proposed block form reveal that the new methods are efficient and highly competitive with existing methods in the literature.http://dx.doi.org/10.1155/2015/343295
collection DOAJ
language English
format Article
sources DOAJ
author F. F. Ngwane
S. N. Jator
spellingShingle F. F. Ngwane
S. N. Jator
A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems
Journal of Applied Mathematics
author_facet F. F. Ngwane
S. N. Jator
author_sort F. F. Ngwane
title A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems
title_short A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems
title_full A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems
title_fullStr A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems
title_full_unstemmed A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value Problems
title_sort family of trigonometrically fitted enright second derivative methods for stiff and oscillatory initial value problems
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2015-01-01
description A family of Enright’s second derivative formulas with trigonometric basis functions is derived using multistep collocation method. The continuous schemes obtained are used to generate complementary methods. The stability properties of the methods are discussed. The methods which can be applied in predictor-corrector form are implemented in block form as simultaneous numerical integrators over nonoverlapping intervals. Numerical results obtained using the proposed block form reveal that the new methods are efficient and highly competitive with existing methods in the literature.
url http://dx.doi.org/10.1155/2015/343295
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