a new algorithm based on lucas polynomials for approximate solution of 2d sobolev equation

The present paper is conducted to propose a combined finite-difference with spectral methods for the numerical solution of two-dimensional sobolev equation. the time variable is approximated by finite difference scheme while the spectral method based on lucas polynomials as basis is employed for discretizing the space variable. by expanding theapproximate solution at collocation points and using matrix operations, the desired model is transformed to an algebraic system of equations. stability analysis of time difference scheme is also investigated. to demonstrate the efficiency and accuracy of the proposed method, a numerical example is given.