Sinc-Galerkin method for solving hyperbolic partial differential equations

Abstract

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation

“…(1) into a nonlinear system of algebraic equations which can be easily solved with Newton's method. Until recently, the Galerkin method has been used to obtain numerical solutions to fractional-order boundary value problems in [14], to the fractional Benney equation in [15], to hyperbolic partial differential equations in [16], to the stochastic heat equation in [17], to fractional sub-diffusion and time-fractional diffusion-wave equations in [18], to nonlinear stochastic integral equations in [19], to ordinary differential equations with non-analytic solution in [20], to the one-dimensional advection-diffusion equation in [21] and to second-order parabolic partial differential equations in [22].…”