Meshless method with ridge basis functions for modified Helmholtz equations

A meshless method for modified Helmholtz equations has been developed by utilizing the collocation method and the ridge basis function interpolation. This method is a truly meshless technique without mesh discretization: it neither needs the computation of integrals, nor requires a partition of the region and its boundary. Moreover, the method is applied to 2-dimensional equations to examine its appropriateness, numerical results are compared to that obtained from other (meshless or mesh-dependent) methods, and influence factors of accuracy for numerical solutions are analyzed.