In this research study, the generalized differential transform scheme has been applied to
simulate impulsive differential equations with the noninteger order. One specific tool of the …

This paper introduces modified collocation techniques that utilize Chebyshev and Legendre
polynomials for solving Thomas–Fermi type equations with integral-type boundary …

Abstract For three-point Lane–Emden–Fowler boundary value problems (LEFBVPs), we
propose two robust algorithms consisting of Bernstein and shifted Chebyshev polynomials …

In this study, we will obtain the approximate solutions of relaxation–oscillation equation by
developing the Taylor matrix method. A relaxation oscillator is a kind of oscillator based on a …

In this paper we introduce a new sequence of polynomials, which follow the same recursive
rule of the well-known Lucas-Lehmer integer sequence. We show the most important …

This article studies Abel integral equations (AIEs) and singular integro-differential equations
(SIDEs) and aims to develop two numerical schemes for them. It also emphasises on the …

This paper deals with the numerical solution of Lane–Emden equations in arising in
astrophysics by using truncated shifted Chebyshev series together with the operational …

Based on Jacobi polynomials, an operational method is proposed to solve the generalized
Abel's integral equations (a class of singular integral equations). These equations appear in …

Abel's integral equation is an efficient singular integral equation that plays an important role
in diverse fields of science. This paper aims to investigate Abel's integral equation and its …

Computer viruses are serious problems for individual and corporate computer systems, and
thus many studies have investigated how to avoid their deleterious effects by creating anti …