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 q...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.展开更多
基金Supported in part by the National Natural Science Foundation of China under Grant No.11021161 and 10928102973 Program of China under Grant No.2011CB80800+2 种基金Chinese Academy of Sciences under Grant No.kjcx-yw-s7project 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
文摘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.
