In this paper three numerical techniques are proposed for solving the system of N-coupled nonlinear Schrödinger (CNLS) equations. Firstly, we obtain a time discrete scheme by approximating the first-order time derivative via the forward finite difference formula, then for obtaining a full discretization scheme, we use the Kansa’s approach to approximate the spatial derivatives via radial basis ...

In this paper a numerical meshless method for solving the radiative transfer equations in a slab medium with an isotropic scattering is considered. The method is based on radial basis functions to approximate the solution of an integral-partial differential equation by using collocation method. For this purpose different applications of RBFs are used. To this end the numerical solutions are obt...

We consider a collocation method using radial functions for the solution of partial differential equations in irregular domains. We use a regularised least squares approach to solve the potentially ill-conditioned problems that may arise. This meshless method is easy to implement and eliminates most of the problems that mesh oriented methods have with irregular boundaries and complicated domain...

An overlapping domain partitioning based on adapting nodes is presented for the meshless-type methods. The decomposition of the domain is carried out based on the distribution of the nodes produced rather than the geometry of the problem. A set of adaptive nodes is first generated using the dimension reduction and equidistributing along the coordinate directions with respect to arc-length monit...

The development of numerical methods for the solution of partial differential equations (PDEs) with nonlocal boundary conditions is important, since such type of problems arise as mathematical models of various real-world processes. We use radial basis function (RBF) collocation technique for the solution of a multidimensional linear elliptic equation with classical Dirichlet boundary condition...

This paper solves the Laplace equation ∆u = 0 on domains Ω ⊂ R by meshless collocation on scattered points of the boundary ∂Ω. In contrast to the Method of Fundamental Solutions, there are no singularities and no artificial boundaries, since we use new singularity–free positive definite kernels which are harmonic in both arguments. In contrast to many other techniques, e.g. the Boundary Point M...

The Multiquadric Radial Basis Function (MQ) Method is a meshless collocation method with global basis functions. It is known to have exponentional convergence for interpolation problems. We descretize nonlinear elliptic PDEs by the MQ method. This results in modest-size systems of nonlinear algebraic equations which can be efficiently continued by standard continuation software such as AUTO and...

In the present work, the numerical solution of two-dimensional variable-order fractional cable (VOFC) equation using meshless collocation methods with thin plate spline radial basis functions is considered. In the proposed methods, we first use two schemes of order O(τ2) for the time derivatives and then meshless approach is applied to the space component. Numerical results obtained ...

In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless discretize the over scattered points instead grids. Radial basis functions (RBFs) popularly used as high accuracy interpolants function values at locations. this paper, we apply polyharmonic splines (PHS) RBF together with appended polynomial and heat conductio...