Che Hussin, Che Haziqah
(2020)
Multi-Step Modified Differential Transform Methods For Hyperbolic Partial Differential Equations.
PhD thesis, Universiti Sains Malaysia.
Abstract
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.
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