Mehdi Dehghan

TL;DR: The main aim is to generalize the Legendre operational matrix to the fractional calculus and reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem.

TL;DR: In this paper, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations (FPDE) with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives, and the results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique.

TL;DR: Several finite difference schemes are discussed for solving the two-dimensional Schrodinger equation with Dirichlet's boundary conditions with the unique advantage of the Barakat and Clark technique, which is unconditionally stable and is explicit in nature.

TL;DR: A numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation is proposed based on using collocation points and approximating the solution employing the thin plate splines radial basis function (RBF).

TL;DR: In this article, a numerical scheme to solve the one-dimensional nonlinear Klein-Gordon equation with quadratic and cubic nonlinearity is proposed, which uses the collocation points and approximates the solution using Thin Plate Splines (TPS) radial basis functions (RBF).