Linear and Nonlinear Integral Equations

Wazwaz, Abdul‐Majid

doi:10.1007/978-3-642-21449-3

Cited by 462 publications

(235 citation statements)

References 4 publications

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“…In this section, we illustrate the Hirota method [24] to acquire another type of solutions-multi soliton solutions of the WZ system. Firstly, we have to apply the following Miura type transformation to obtain the WZ system's reduced form's operator form…”

Section: Hirota Methodsmentioning

confidence: 99%

On soliton solutions of the Wu-Zhang system

et al. 2016

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Section: Hirota Methodsmentioning

confidence: 99%

On soliton solutions of the Wu-Zhang system

et al. 2016

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“…In fact the above process, Equation (18), is a multiple-step successive approximations method and it is equivalent to multiple-step Picard iteration method (Djang, 1948;Lal and Moffatt, 1982;Wazwaz, 2011) with DTM solution as the zeroth approximation of y m (t).…”

Section: Enhanced Msdtmmentioning

confidence: 99%

A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems

El‐Zahar¹,

Habib²,

Rashidi³

et al. 2015

American Journal of Applied Sciences

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Abstract:In this study, a comparison among three semi-analytical numerical integration algorithms for solving stiff ODE systems is presented. The algorithms are based on Differential Transform Method (DTM) which are Multiple-Step DTM (MsDTM), Enhanced MsDTM (EMsDTM) and MsDTM with Padé approximants (MsDTM-P). These methods can be classified as explicit one step semi-analytical numerical integration methods. The error and stability analysis of each method is presented. New important relationships among the methods are introduced. To demonstrate our results, a comparison of the accuracy, stability and computational efficiency of the methods is presented through solving some linear and nonlinear problems arising in applied science and engineering.

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“…The problem was solved by using the series solution method in [28]. We apply the present method for N = 5, 8, 9.…”

Section: Example 1 [34] Our First Problem Ismentioning

confidence: 99%

An operational matrix method for solving linear Fredholm--Volterra integro-differential equations

Yüzbaşı¹,

Ismailov²

2018

Turk J Math

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The aim of this paper is to propose an efficient method to compute approximate solutions of linear Fredholm-Volterra integro-differential equations (FVIDEs) using Taylor polynomials. More precisely, we present a method based on operational matrices of Taylor polynomials in order to solve linear FVIDEs. By using the operational matrices of integration and product for the Taylor polynomials, the problem for linear FVIDEs is transformed into a system of linear algebraic equations. The solution of the problem is obtained from this linear system after the incorporation of initial conditions. Numerical examples are presented to show the applicability and the efficiency of the method. Wherever possible, the results of our method are compared with those yielded by some other methods.

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Linear and Nonlinear Integral Equations

Cited by 462 publications

References 4 publications

On soliton solutions of the Wu-Zhang system

On soliton solutions of the Wu-Zhang system

A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems

An operational matrix method for solving linear Fredholm--Volterra integro-differential equations

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