Expansion in series of exponential polynomials of mean-periodic functions

Applied Mathematical Modelling

2013

a b s t r a c tIn this paper, a new matrix method based on exponential polynomials and collocation points is proposed for solutions of pantograph equations with linear functional arguments under the mixed conditions. Also, an error analysis technique based on residual function is developed for the suggested method. Some examples are given to demonstrate the validity and applicability of the method and the comparisons are made with existing results.

Section: Introductionmentioning

confidence: 99%

An exponential approximation for solutions of generalized pantograph-delay differential equations

Applied Mathematical Modelling

2013

“…On the other hand, exponential polynomials or exponential functions have interesting applications in many optical and quantum electronics [19], some nonlinear phenomena modeled by partial differential equations [20], many statistical discussions (especially in data analysis) [21], the safety analysis of control synthesis [22], the problem of expressing mean-periodic functions [23], and the study of spectral synthesis [24,25]. These polynomials are based on the exponential base set {1, − , −2 , .…”

Section: Introductionmentioning

confidence: 99%

Exponential Collocation Method for Solutions of Singularly Perturbed Delay Differential Equations

Abstract and Applied Analysis

2013

This paper deals with the singularly perturbed delay differential equations under boundary conditions. A numerical approximation based on the exponential functions is proposed to solve the singularly perturbed delay differential equations. By aid of the collocation points and the matrix operations, the suggested scheme converts singularly perturbed problem into a matrix equation, and this matrix equation corresponds to a system of linear algebraic equations. Also, an error analysis technique based on the residual function is introduced for the method. Four examples are considered to demonstrate the performance of the proposed scheme, and the results are discussed.

“…On the other hand, exponential polynomials or exponential functions have interesting applications in many optical and quantum electronics , some nonlinear phenomena modeled by partial differential equations , many statistical discussions (especially in data analysis) , the safety analysis of control synthesis , the problem of expressing mean‐periodic functions , and the study of spectral synthesis . These polynomials are based on the exponential base set {1, e − x , e −2 x , … }.…”

Section: Introductionmentioning

confidence: 99%

An exponential matrix method for solving systems of linear differential equations

Math Methods in App Sciences

2012

This paper presents an exponential matrix method for the solutions of systems of high‐order linear differential equations with variable coefficients. The problem is considered with the mixed conditions. On the basis of the method, the matrix forms of exponential functions and their derivatives are constructed, and then by substituting the collocation points into the matrix forms, the fundamental matrix equation is formed. This matrix equation corresponds to a system of linear algebraic equations. By solving this system, the unknown coefficients are determined and thus the approximate solutions are obtained. Also, an error estimation based on the residual functions is presented for the method. The approximate solutions are improved by using this error estimation. To demonstrate the efficiency of the method, some numerical examples are given and the comparisons are made with the results of other methods. Copyright © 2012 John Wiley & Sons, Ltd.