A new collocation scheme for solving hyperbolic equations of second order in a semi-infinite domain

ملخص البحث

This paper reports a new fully collocation algorithm for the numerical solution of hyperbolic partial differential equations (PDEs) of second order in a semi-infinite domain, using Jacobi rational Gauss-Radau collocation (JR-GR-C) method. The widely applicable, efficiency, and high accuracy are the more advantages of the collocation method. The series expansion in Jacobi rational functions is the main step for solving the mentioned problems. The expansion coefficients are then determined by reducing the hyperbolic equations with its boundary and initial conditions to a system of algebraic equations for these coefficients. This system may be solved analytically or numerically in step-by-step manner by using Newtons iterative method. Numerical results are consistent with the theoretical analysis and indicating the high accuracy and effectiveness of this algorithm.

الكلمات المفتاحيه

Hyperbolic PDEs; Jacobi rational functions; Collocation method; Semi-infinite domain; Gauss-Radau quadrature