This paper presents a new approximate method of Abel differential equation. By using the shifted Chebyshev expansion of the unknown function, Abel differential equation is approximately transformed to a system of nonlinear ...

In this study, a new collocation method based on the Bernstein polynomials is introduced for the approximate solution of the pantograph-type differential equations with retarded case or advanced case. In addition, the ...

In this study, a new collocation method based on the Bernstein polynomials is introduced for the approximate solution of a class of linear Volterra integro-differential equations with weakly singular kernel. If the exact ...

The aim of this article is to present an efficient numerical procedure for solving nonlinear integro-differential equations. Our method depends mainly on a Taylor expansion approach. This method transforms the integro-differential ...

In this study, a practical matrix method is presented to find an approximate solution for high-order linear Fredholm integro-differential equations with piecewise intervals under the initial boundary conditions in terms ...

This paper presents a numerical method for the approximate solution of mth-order linear delay difference equations with variable coefficients under the mixed conditions in terms of Laguerre polynomials. The aim of this ...

The purpose of this study is to give a Hermite polynomial approximation for the solution of m(th) order linear differential-difference equations with variable coefficients under mixed conditions. For this purpose, a new ...

An approximate method for solving higher-order linear complex differential equations in elliptic domains is proposed. The approach is based on a Taylor collocation method, which consists of the matrix represantation of ...

In this work, high order pantograph type linear functional differential equations with hybrid proportional and variable delays is approximately solved by the modified Taylor matrix method. With this method these functional ...

In this paper, a numerical power series algorithm which is based on the improved Taylor matrix method is introduced for the approximate solution of Abel-type differential equations and also, Riccati differential equations. ...