A new numerical method to solve pantograph delay differential equations with convergence analysis

Abstract The main aim presented in this article is to provide an efficient transferred Legendre pseudospectral method for solving pantograph delay differential equations. At the first step, we transform the problem into a continuous-time optimization problem and then utilize a transferred Legendre pseudospectral method to discretize the problem. By solving this discrete problem, we can attain the pointwise and continuous estimated solutions for the major pantograph delay differential equation. The convergence of method has been considered. Also, numerical experiments are described to show the performance and precision of the presented technique. Moreover, the obtained results are compared with those from other techniques

Orthoexponential polynomial solutions of delay pantograph differential equations with residual error estimation

In this paper, a new matrix method based on orthogonal exponential (orthoexponential) polynomials and collocation points is proposed to solve the high-order linear delay differential equations with linear functional arguments under the mixed conditions. The convenience is that orthoexponential polynomials have shown to be effective in approximating a given function, fast and efficiently. An error analysis technique based on residual function is developed and applied to four problems to demonstrate the validity and applicability of the proposed method. It is confirmed that the present method yields quite acceptable results and the accuracy of the solution can significantly be increased by error correction and residual function. (C) 2015 Elsevier Inc. All rights reserved

Orthoexponential polynomial solutions of delay pantograph differential equations with residual error estimation

In this paper, a new matrix method based on orthogonal exponential (orthoexponential) polynomials and collocation points is proposed to solve the high-order linear delay differential equations with linear functional arguments under the mixed conditions. The convenience is that orthoexponential polynomials have shown to be effective in approximating a given function, fast and efficiently. An error analysis technique based on residual function is developed and applied to four problems to demonstrate the validity and applicability of the proposed method. It is confirmed that the present method yields quite acceptable results and the accuracy of the solution can significantly be increased by error correction and residual function. (C) 2015 Elsevier Inc. All rights reserved