Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations

We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector met...

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Main Authors: S. N. Jator, F. F. Ngwane, N. O. Kirby
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/1535430
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spelling doaj-3bcd3da8a300428887607f24290e6f802020-11-24T21:33:23ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/15354301535430Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential EquationsS. N. Jator0F. F. Ngwane1N. O. Kirby2Department of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USADepartment of Mathematics, University of South Carolina, Salkehatchie, Walterboro, SC 29488, USADepartment of Mathematics and Statistics, Austin Peay State University, Clarksville, TN 37044, USAWe present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method’s relative accuracy and efficiency.http://dx.doi.org/10.1155/2019/1535430
collection DOAJ
language English
format Article
sources DOAJ
author S. N. Jator
F. F. Ngwane
N. O. Kirby
spellingShingle S. N. Jator
F. F. Ngwane
N. O. Kirby
Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations
Mathematical Problems in Engineering
author_facet S. N. Jator
F. F. Ngwane
N. O. Kirby
author_sort S. N. Jator
title Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations
title_short Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations
title_full Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations
title_fullStr Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations
title_full_unstemmed Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations
title_sort functionally fitted block method for solving the general oscillatory second-order initial value problems and hyperbolic partial differential equations
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description We present a block hybrid functionally fitted Runge–Kutta–Nyström method (BHFNM) which is dependent on the stepsize and a fixed frequency. Since the method is implemented in a block-by-block fashion, the method does not require starting values and predictors inherent to other predictor-corrector methods. Upon deriving our method, stability is illustrated, and it is used to numerically solve the general second-order initial value problems as well as hyperbolic partial differential equations. In doing so, we demonstrate the method’s relative accuracy and efficiency.
url http://dx.doi.org/10.1155/2019/1535430
work_keys_str_mv AT snjator functionallyfittedblockmethodforsolvingthegeneraloscillatorysecondorderinitialvalueproblemsandhyperbolicpartialdifferentialequations
AT ffngwane functionallyfittedblockmethodforsolvingthegeneraloscillatorysecondorderinitialvalueproblemsandhyperbolicpartialdifferentialequations
AT nokirby functionallyfittedblockmethodforsolvingthegeneraloscillatorysecondorderinitialvalueproblemsandhyperbolicpartialdifferentialequations
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