An Efficient Numerical Method For A Class of Boundary Value Problems, Based on Shifted Jacobi-Gauss Collocation Scheme

This paper proposes a numerical method to deal with the two-dimensional hyperbolic equations with nonlocal integral conditions. the nonlocal integral equation usually is of major challenge in the frame work of the numerical solutions of partial di erential equations. the method bene ts from collocation radial basis function method, the generalized thin plate splines (gtps) radial basis functions are used. therefore, it does not require any struggle to determine shape parameter (in other rbfs, it is time- consuming step). the present technique is one of the truly meshless methods in where it does not require any background integration cells over local or global domains and it is in contrast to weak form methods in where all integrations are carried out locally or globally over quadrature domains of regular shapes, such as lines in one dimensions, circles or squares in two dimensions and spheres or cubes in three dimensions. the obtained results for some numerical examples reveal that the proposed technique is very e ective, convenient and quite accurate to such considered problems.