Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations

In this thesis, we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with...

Full description

Saved in:

Bibliographic Details
Main Author:	Che Hussin, Che Haziqah
Format:	Thesis
Language:	English
Published:	2020
Subjects:	QA1 Mathematics (General)
Online Access:	http://eprints.usm.my/52549/1/Pages%20from%2026102020%20FINAL%20VERSION%20PHD%20THESIS%20-%20CHE%20HAZIQAH%20CHE%20HUSSIN.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-usm-ep.52549
record_format	uketd_dc
spelling	my-usm-ep.525492022-05-20T02:08:15Z Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations 2020-10 Che Hussin, Che Haziqah QA1 Mathematics (General) In this thesis, we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. The MMRDTM is presented with some modification of the Reduced Differential Transformation Method (RDTM) with multi-step approach and its nonlinear term is replaced by the Adomian polynomials. Therefore, the nonlinear initial value problem can easily be solved with less computational effort. Besides that, the multi-step approach produces a solution in fast converging series that converges the solution in a wide time area. In this study, three types of equations that describe solitary waves are considered: nonlinear Schrödinger (NLS) equation, nonlinear Korteweg-de Vries (NKdV) equation and nonlinear Klein-Gordon equation (NKG) equation. These equations are solved by using the MMRDTM. Besides that, we investigated the feasibility of applying the MMRDTM for the fractional NLS equations, fractional NKdV equations and fractional NKG equations. 2020-10 Thesis http://eprints.usm.my/52549/ http://eprints.usm.my/52549/1/Pages%20from%2026102020%20FINAL%20VERSION%20PHD%20THESIS%20-%20CHE%20HAZIQAH%20CHE%20HUSSIN.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA1 Mathematics (General)
spellingShingle	QA1 Mathematics (General) Che Hussin, Che Haziqah Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations
description	In this thesis, we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. The MMRDTM is presented with some modification of the Reduced Differential Transformation Method (RDTM) with multi-step approach and its nonlinear term is replaced by the Adomian polynomials. Therefore, the nonlinear initial value problem can easily be solved with less computational effort. Besides that, the multi-step approach produces a solution in fast converging series that converges the solution in a wide time area. In this study, three types of equations that describe solitary waves are considered: nonlinear Schrödinger (NLS) equation, nonlinear Korteweg-de Vries (NKdV) equation and nonlinear Klein-Gordon equation (NKG) equation. These equations are solved by using the MMRDTM. Besides that, we investigated the feasibility of applying the MMRDTM for the fractional NLS equations, fractional NKdV equations and fractional NKG equations.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Che Hussin, Che Haziqah
author_facet	Che Hussin, Che Haziqah
author_sort	Che Hussin, Che Haziqah
title	Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations
title_short	Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations
title_full	Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations
title_fullStr	Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations
title_full_unstemmed	Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations
title_sort	multi-step modified differential transform methods for hyperbolic partial differential equations
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik
publishDate	2020
url	http://eprints.usm.my/52549/1/Pages%20from%2026102020%20FINAL%20VERSION%20PHD%20THESIS%20-%20CHE%20HAZIQAH%20CHE%20HUSSIN.pdf
_version_	1747822190046216192

Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations

Similar Items