Hafez, RMBhrawy, Ali HBhrawy, Ali HDoha, Eid H2019-12-012019-12-012017-040168-9673https://doi.org/10.1007/s10255-017-0660-7https://link.springer.com/article/10.1007/s10255-017-0660-7Accession Number: WOS:000400856100005A 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.en-USUniversity for OPERATIONAL MATRIXPROPORTIONAL DELAYSPSEUDOSPECTRAL METHODSSEMIINFINITE INTERVALCHEBYSHEV TAU-METHODBOUNDARY-VALUE-PROBLEMSVARIATIONAL ITERATION METHODINITIAL-VALUE PROBLEMSGAUSS COLLOCATION METHODORDINARY DIFFERENTIAL-EQUATIONSconvergence analysisJacobi rational functionsJacobi-Gauss quadraturecollocation methoddelay equationmulti-pantograph equationArticlehttps://doi.org/10.1007/s10255-017-0660-7