On the Numerical Solution of Generalized Pantograph Equation

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

A Taylor operation method for solutions of generalized pantograph type delay differential equations

Abstract: In this paper, a new operational matrix method based on the Taylor polynomials is presented to solve generalized pantograph type delay differential equations. The method is based on operational matrices of integration and product for Taylor polynomials. These matrices are obtained by using the best approximation of function by the Taylor polynomials. The advantage of the method is tha...

The Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials

‎In this paper‎, ‎we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays‎. ‎Constant or pantograph delays may appear in state-control or both‎. ‎We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then‎, ‎these are utilized to reduce the solution of optimal control with constant...

Stability of the Discretized Pantograph Differential Equation

In this paper we study discretizations of the general pantograph equation y'(t) = ay(t) + by(6(t)) + cy'((t)), f>0, y(0)=y0, where a , b , c , and yo are complex numbers and where 9 and <¡> are strictly increasing functions on the nonnegative reals with 0(0) = <^>(0) = 0 and 8(t) < t, 4>(t) < t for positive /. Our purpose is an analysis of the stability of the numerical solution with trapezo...

Numerical solution of fuzzy differential equations under generalized differentiability by fuzzy neural network

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large eld called ne...