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A Tutorial to Approximately Invert the sumudu Transform

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Applied Mathematics 2019年第11期10卷 1004-1028页

作者： Glen Atlas John K.-J. Li Adam Work Department of Anesthesiology Rutgers New Jersey Medical School Newark NJ USA Department of Biomedical Engineering Stevens Institute of Technology Hoboken NJ USA Department of Biomedical Engineering Rutgers University Piscataway NJ USA

Unlike the traditional Laplace transform, the sumudu transform of a function, when approximated as a power series, may be readily inverted using factorial-based coefficient diminution. This technique offers straightforward computational advantages for approximate range-limited numerical solutions of certain ordinary, mixed, and partial linear differential and integro-differential equations. Furthermore, discrete convolution (the Cauchy product), may also be utilized to assist in this approximate inversion method of the sumudu transform. Illustrative examples are provided which elucidate both the applicability and limitations of this method.

关键词： sumudu Transform Double Series Discrete Convolution Cauchy Product

Implementation of the Homotopy Perturbation sumudu Transform Method for Solving Klein-Gordon Equation

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Applied Mathematics 2015年第3期6卷 617-628页

作者： Amr M. S. Mahdy Adel S. Mohamed Ahmad A. H. Mtawa Department of Mathematics Faculty of Science Zagazig University Zagazig Egypt Department of Mathematics Faculty of Science Benghize University Almarj Libya

This paper extends the homotopy perturbation sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. The convergence of the HPSTM solutions to the exact solutions is shown. As a novel application of homotopy perturbation sumudu transform method, the presented work showed some essential difference with existing similar application four classical examples also highlighted the significance of this work.

关键词： Mittag-Leffler Functions Caputo Derivative sumudu Transform Homotopy Perturbation Method Klein-Gordon Equation

Exact Solution of Fractional Black-Scholes European Option Pricing Equations

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Applied Mathematics 2018年第1期9卷 86-100页

作者： Maryeme Ouafoudi Fei Gao Mathematics Department Wuhan University of Technology Wuhan China

We introduce two algorithms in order to find the exact solution of the nonlinear Time-fractional Partial differential equation, in this research work. Those algorithms are proposed in the following structure: The Modified Homotopy Perturbation Method (MHPM), The Homotopy Perturbation and sumudu Transform Method. The results achieved using the both methods are the same. However, we calculate the approached theoretical solution of the Black-Scholes model in the form of a convergent power series with a regularly calculated element. Finally, we propose a descriptive example to demonstrate the efficiency and the simplicity of the methods.

关键词： Homotopy Perturbation Method Modified Homotopy Perturbation Method sumudu Transform Black-Scholes Equations

Laplace Transform Analytical Restructure

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Applied Mathematics 2013年第6期4卷 919-932页

作者： Fethi Bin Muhammad Belgacem Rathinavel Silambarasan Department of Mathematics Faculty of Basic Education PAAET Shaamyia Kuwait M. S. Software Engg SITE V. I. T. University Vellore India

In this paper, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods. We show that the said transform can be simply calculated by differentiation of the original function. Various analytic consequent results are given. The simplicity and efficacy of the method are illustrated through many examples with shown Maple graphs, and transform tables are provided. Finally, a new infinite series representation related to Laplace transforms of trigonometric functions is proposed.

关键词： Laplace Transform Natural Transform sumudu Transform