Also the obtained numerical results show the applicability of the proposed three methods to find the numerical solution of the KGS equations. At the end of this paper, we provide some examples on one, two and three-dimensions for obtaining numerical simulations. Robert Schaback, Kernel-based Meshless Methods, Lecture Notes, Goettingen, 2011. Also the GMLS technique yields a well-conditioned linear system, because a shifted and scaled polynomial basis will be used. Fasshauer, Meshfree Approximation Methods with MATLAB. But when we employ PS method (Fasshauer, 2007), the matrix of coefficients in the obtained linear system of algebraic equations is well-conditioned. As is well-known, the use of Kansa’s approach makes the coefficients matrix in the above linear system of algebraic equations to be ill-conditioned and we applied LU decomposition technique. Applying three techniques reduces the solution of the one, two and three dimensional partial differential equations to the solution of linear system of algebraic equations. Meshfree approximation methods, such as radial basis. The proposed methods do not require any background mesh or cell structures, so they are based on a meshless approach. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. 1(c), dashed and dotted line, is a function approximation problem in a high dimensional space. First, the time derivative of the mentioned equation will be approximated using an implicit method based on Crank–Nicolson scheme then Kansa’s approach, RBFs-Pseudo-spectral (PS) method and generalized moving least squares (GMLS) method will be used to approximate the spatial derivatives. Polynomial preconditioners for Krylov subspace methods came into vogue in the late 1970s with the advent of vector computers but they are currently out of favor because of their limited effectiveness and robustness, especially for nonsymmetric problems. Conformation analysis in the view of Fig. In the present study, three numerical meshless methods are being considered to solve coupled Klein–Gordon–Schrödinger equations in one, two and three dimensions.