We present a method to solve the Helmholtz equation for a non-homogeneous membrane with Dirichlet boundary conditions at the border of arbitrary two-dimensional domains. The method uses a collocation approach based on a set of localized functions, called ”little sinc functions”, which are used to discretize two-dimensional regions. We have performed extensive numerical tests and we have compare...

Abstract In this paper, a nonclassical sinc collocation method is constructed for the numerical solution of systems second-order integro-differential equations Volterra and Fredholm types. The novelty approach based on using new weight function instead classic ones. functions used to reduce system algebraic equations. Furthermore, convergence proposed theoretically, showing that converges expon...

Tthis paper, is concerned with obtaining numerical solutions for a class of convection-diffusion equations (CDEs) with variable coefficients. Our approaches are based on collocation methods. These approaches implementing all four kinds of shifted Chebyshev polynomials in combination with Sinc functions to introduce an approximate solution for CDEs . This approximate solution can be expressed as...