Numerical Algorithm for Solving Multi-Pantograph Delay Equations on the Half-line Using Jacobi Rational Functions with Convergence Analysis  

作　　者：Eid H. DOHA Ali H. BHRAWY Ramy M. HAFEZ 

机构地区：[1]Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt [2]Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia [3]Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt [4]Department of Mathematics, Alwagjh University College, University of Tabuk , Tabuk, Saudi Arabia [5]Department of Basic Science, Institute of Information Technology, Modern Academy, Cairo, Egypt

出　　处：《Acta Mathematicae Applicatae Sinica》2017年第2期297-310,共14页应用数学学报（英文版）

基　　金：Supported in part by the National Natural Science Foundation of China under Grant No.11021161 and 10928102;973 Program of China under Grant No.2011CB80800;Chinese Academy of Sciences under Grant No.kjcx-yw-s7;project grant of “Center for Research and Applications in Plasma Physics and Pulsed Power Technology,PBCT-Chile-ACT 26”;Direccion de Programas de Investigacion,Universidad de Talca,Chile

摘　　要：A new spectral Jacobi rational-Gauss collocation （JRC） method is proposed for solving the multi- pantograph delay differential equations on the half-line. The method is based on Jacobi rational functions and Gauss quadrature integration formula. The main idea for obtaining a semi-analytical solution for these equations is essentially developed by reducing the pantograph equations with their initial conditions to systems of algebraic equations in the unknown expansion coefficients. The convergence analysis of the method is analyzed. The method possesses the spectral accuracy. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Indeed, the present method is compared favorably with other methods.A new spectral Jacobi rational-Gauss collocation （JRC） method is proposed for solving the multi- pantograph delay differential equations on the half-line. The method is based on Jacobi rational functions and Gauss quadrature integration formula. The main idea for obtaining a semi-analytical solution for these equations is essentially developed by reducing the pantograph equations with their initial conditions to systems of algebraic equations in the unknown expansion coefficients. The convergence analysis of the method is analyzed. The method possesses the spectral accuracy. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Indeed, the present method is compared favorably with other methods.

关 键 词：multi-pantograph equation delay equation collocation method Jacobi-Gauss quadrature Jacobirational functions convergence analysis 

分 类 号：O175[理学—数学]