The coupled viscous Burgers' equations have been an interesting and hot topic in
mathematics and physics for a long time, and they have been solved by many methods. In …

In this paper, using the collocation method we solve the nonlinear fractional integro-
differential equations (NFIDE) of the form: f (t, y (t), a CD t α 0 y (t),…, a CD t α ry (t))= λ G (t, y …

Abstract A Jacobi–Gauss–Lobatto collocation (J-GL-C) method, used in combination with
the implicit Runge–Kutta method of fourth order, is proposed as a numerical algorithm for the …

In this paper, an efficient and accurate numerical method is presented for solving two types
of fractional partial differential equations. The fractional derivative is described in the Caputo …

In this paper, a new set of functions called fractional alternative Legendre is defined for
solving nonlinear fractional integro-differential equations. The concept of the fractional …

A numerical technique for solving nonlinear ordinary differential equations on a semi-infinite
interval is presented. We solve the Thomas–Fermi equation by the Sinc-Collocation method …

In this paper, we study the numerical solution to time‐fractional partial differential equations
with variable coefficients that involve temporal Caputo derivative. A spectral method based …

The inverse problem of determining the unknown source for a fractional diffusion equation is
studied. This problem is ill-posed in the sense of Hadamard, ie, small changes in the …

In this paper, we study the simulation of nonlinear Schrödinger equation in one, two and
three dimensions. The proposed method is based on a time-splitting method that …

The inverse problem of identifying the diffusion coefficient in the one‐dimensional parabolic
heat equation is studied. We assume that the information of Dirichlet boundary conditions …