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. The proposed methods do not require any background mesh or cell structures, so they are based on a meshless approach. 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.
In the present study, three numerical meshless methods are being considered to solve coupled Klein–Gordon–Schrödinger equations in one, two and three dimensions.
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