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Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

Computer Modeling in Engineering & Sciences 2024年第2期138卷 1593-1616页

作者： Rania Saadah Mohammed Amleh Ahmad Qazza shrideh al-omari Ahmet Ocak Akdemir Department of Mathematics Faculty of ScienceZarqa UniversityZarqa13110Jordan Department of Mathematics Faculty of ScienceAl-Balqa Applied UniversityAmman11134Jordan Department of Mathematics Faculty of Science and LettersAgri Ibrahim莈鏴n UniversityAgri04100Turkey

In this study,we aimto investigate certain triple integral transformand its application to a class of partial *** discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution ***, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations ***,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

关键词： ARA transform double ARA transform triple ARA transform partial differential equations integral transform

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On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

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Computer Modeling in Engineering & Sciences 2023年第9期136卷 3121-3139页

作者： Rania Saadeh Ahmad Qazza aliaa Burqan shrideh al-omari Department of Mathematics Zarqa UniversityZarqa13110Jordan Department of Mathematics Faculty of ScienceAl-Balqa Applied UniversityAmman11134Jordan

This paper aims to investigate a new efficient method for solving time fractional partial differential *** this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition ***,certain accurate solutions for time-fractional partial differential equations have been *** under concern demandsmore simple calculations and fewer efforts compared to the ***,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential ***,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing ***,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon *** and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

关键词： Caputo derivative fractional differential equations formable transform time-fractional klein-gordon equation decomposition method

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Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some Error Analysis

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Computer Modeling in Engineering & Sciences 2022年第1期130卷 299-313页

作者： Radwan Abu-Gdairi Shatha Hasan shrideh al-omari Mohammad al-Smadi Shaher Momani Department of Mathematics Faculty of ScienceZarqa UniversityZarqa13132Jordan Department of Applied Science Ajloun CollegeAl-Balqa Applied UniversityAjloun26816Jordan Department of Physics and Basic Sciences Faculty of Engineering TechnologyAl-Balqa Applied UniversityAmman11134Jordan Nonlinear Dynamics Research Center(NDRC) Ajman UniversityAjman20550United Arab Emirates Department of Mathematics Faculty of ScienceThe University of JordanAmman11942Jordan

In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential *** solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev *** the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties ***,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are *** this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and *** gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.

关键词： Multi-step approach reproducing kernel Hilbert space method stiffness system error analysis numerical solution

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