Shifted Legendre approximation with the residual correction to solve pantograph-delay type differential equations

Fractional differential equations with Legendre polynomials

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...

Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type

Xiuxiu Xu and Qiumei Huang Beijing Institue for Scientific and Engineering Computing, Beijing University of Technology, Beijing 100124, China Email: [email protected], [email protected] Hongtao Chen School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen 361005, China Email: ch...

A Legendre-gauss Collocation Method for Nonlinear Delay Differential Equations

In this paper, we introduce an efficient Legendre-Gauss collocation method for solving nonlinear delay differential equations with variable delay. We analyze the convergence of the single-step and multi-domain versions of the proposed method, and show that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. We also make numerical comparison with other ...

New Operational Matrix For Shifted Legendre Polynomials and Fractional Differential Equations With Variable Coefficients

This paper is devoted to study a computation scheme to approximate solution of fractional differential equations(FDEs) and coupled system of FDEs with variable coefficients. We study some interesting properties of shifted Legendre polynomials and develop a new operational matrix. The new matrix is used along with some previously derived results to provide a theoretical treatment to approximate ...