Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations

Weighted Block Runge-Kutta (WBRK) methods are derived to solve first order stiff ordinary differential equations (ODEs). The proposed methods approximate solutions at two points concurrently in a block at each step. Three sets of weight are chosen and implemented to the WBRK methods. Stability regio...

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Main Author:	Jana Aksah, Saufianim
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Computer science Numerical analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/75482/1/FS%202016%2022%20-%20IR.pdf
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id	my-upm-ir.75482
record_format	uketd_dc
spelling	my-upm-ir.754822019-11-26T01:45:33Z Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations 2016-05 Jana Aksah, Saufianim Weighted Block Runge-Kutta (WBRK) methods are derived to solve first order stiff ordinary differential equations (ODEs). The proposed methods approximate solutions at two points concurrently in a block at each step. Three sets of weight are chosen and implemented to the WBRK methods. Stability regions of the WBRK methods with each set of weight are constructed by using MAPLE14. Stability properties of the proposed methods with each weight show that the methods are suitable for solving stiff ODEs. Numerical results are presented and illustrated in the form of efficiency curves. Performances of the WBRK methods in terms of maximum error and computational time are compared with the third order Runge-Kutta (RK3) and the modified weighted RK3 method based on centroidal mean (MWRK3CeM). These methods are tested with problems of single and system of first order stiff ODEs. Comparison of the proposed methods between sets of weight is also analyzed. The numerical results are obtained by using MATLAB R2011a. Numerical results generated show that the WBRK methods obtained better accuracy and less computational time than the RK3 and MWRK3CeM method. Computer science Numerical analysis 2016-05 Thesis http://psasir.upm.edu.my/id/eprint/75482/ http://psasir.upm.edu.my/id/eprint/75482/1/FS%202016%2022%20-%20IR.pdf text en public masters Universiti Putra Malaysia Computer science Numerical analysis
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Computer science Numerical analysis
spellingShingle	Computer science Numerical analysis Jana Aksah, Saufianim Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations
description	Weighted Block Runge-Kutta (WBRK) methods are derived to solve first order stiff ordinary differential equations (ODEs). The proposed methods approximate solutions at two points concurrently in a block at each step. Three sets of weight are chosen and implemented to the WBRK methods. Stability regions of the WBRK methods with each set of weight are constructed by using MAPLE14. Stability properties of the proposed methods with each weight show that the methods are suitable for solving stiff ODEs. Numerical results are presented and illustrated in the form of efficiency curves. Performances of the WBRK methods in terms of maximum error and computational time are compared with the third order Runge-Kutta (RK3) and the modified weighted RK3 method based on centroidal mean (MWRK3CeM). These methods are tested with problems of single and system of first order stiff ODEs. Comparison of the proposed methods between sets of weight is also analyzed. The numerical results are obtained by using MATLAB R2011a. Numerical results generated show that the WBRK methods obtained better accuracy and less computational time than the RK3 and MWRK3CeM method.
format	Thesis
qualification_level	Master's degree
author	Jana Aksah, Saufianim
author_facet	Jana Aksah, Saufianim
author_sort	Jana Aksah, Saufianim
title	Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations
title_short	Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations
title_full	Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations
title_fullStr	Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations
title_full_unstemmed	Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations
title_sort	weighted block runge-kutta methods for solving stiff ordinary differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/75482/1/FS%202016%2022%20-%20IR.pdf
_version_	1747813057166311424

Weighted Block Runge-Kutta methods for solving stiff ordinary differential equations

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