A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation

On the Numerical Solution of Generalized Pantograph Equation

Absrtact: In this study, a numerical algorithm for solving a generalization of a functional differential equation known as the pantograph equation is presented. Firstly, the proposed algorithm produces an approximate polynomial solution as a power series for the problem. Then, we transform the obtained power series into Padé series form to obtain an approximate polynomial of an arbitrary order ...

A New Generalized Laguerre-gauss Collocation Scheme for Numerical Solution of Generalized Fractional Pantograph Equations

A.H. BHRAWY1,2, A.A. AL-ZAHRANI3, Y.A. ALHAMED3, D. BALEANU3,4,5 1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia E-mail: [email protected] 2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt 3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, J...

Numerical Solution of the Lane-Emden Equation Based on DE Transformation via Sinc Collocation Method

In this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ ‎equation‎. ‎Numerical examples show the accuracy of the method.‎ ‎Also‎, ‎some remarks with respect to run-time‎, computational cost‎ ‎and implementation are discussed.

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

Using operational matrix for numerical solution of fractional differential equations

In this article, we have discussed a new application of modification of hat functions on nonlinear multi-order fractional differential equations. The operational matrix of fractional integration is derived and used to transform the main equation to a system of algebraic equations. The method provides the solution in the form of a rapidly convergent series. Furthermore, error analysis of the pro...