Walsh stretch matrices and functional differential equations

Abstract

SI S N S i n g . "A modified algorithm for ~nvertihiht> in nonlinear bkztsmr." JE-EE [61 R W . Brm.kett and M. D hiesarob~c. "The rsproducihdit? of mult~~ariabls byten?>." [?I Xi K. Sain and I. L Mas??. "Inkertihiht) of linear lmc-lnvanant d>nam~~aI [X] L. M Silvrrman. "Inversion of multivanahle hncar s?*tem,." I E E E Tram .4~10mur (91 L. M. Sllvmnan and H. I. Payne. "Input-output \tmc'turc of linear >>stems with 7rmu .Auromur. Conrr.,4bsrrucr -This correspondence presents a new operational matrix for "Stretch" via Walsh functions and discusses some interesting properlies of this matrix and its role in the solution of certain functional differential equations. The solutions of differential equations are obtained in a series of Walsh functions. The results are piecewise constant with minimal meansquare error. The single term approximation combined with the technique of extension [SI reduces the computational effort to a minimum.Abstract--A sufficient condition for the inrertibility of n~ultivariable distributed parameter systems described b! partial differential equations of parabolic tvpe ic presented. For invertible ystems. distributed inverse systems are canctructed. An example is worked out.

Numerical Solution of Pantograph-Type Delay Differential Equations Using Perturbation-Iteration Algorithms

“…Equation (32) can be written in the following form: Journal of Applied Mathematics Walsh series method [26] DUSF series method [27] Hermite series method [3] Taylor series method [4] Laguerre matrix method [28] PIA ( …”

A taylor collocation method for solving high-order linear pantograph equations with linear functional argument

“…(23) with N = 6, 7, 8, by presented method. The previous results of Rao Palanisamy by Wals series approach [18], Hwang by delay unit step function (DUSF) series approach [19] and Hwang et al by Laguerre series approach [20] are also given in Table I for comparison. which has the exact solution y(t) = e t .…”

A numerical method for solving systems of higher order linear functional differential equations

“…These systems are di cult to solve analytically.In this paper we consider the systems of linear functional di erential equations [1][2][3][4][5][6][7][8][9] including the term y(αx + β) and advance-delay in derivatives of y . To obtain the approximate solutions of those systems, we present a matrixcollocation method by using Müntz-Legendre polynomials and the collocation points.…”

“…In physics, chemistry, biology and engineering, a lot of problems are modelled by di erential equations, delay differential equations [10][11][12][13] and their systems [1][2][3][4][5][6][7][8][9][14][15][16][17].…”