The aim of this manuscript is to investigate an accurate discretization method to solve the
one-, two-, and three-dimensional highly nonlinear Bratu-type problems. By discretization of …

In this article we introduce a numerical method, named Gegenbauer wavelets method,
which is derived from conventional Gegenbauer polynomials, for solving fractional initial and …

In this paper we propose a new iterative finite difference (IFD) scheme based on the Newton–
Raphson–Kantorovich approximation method in function space to solve the classical one …

In this manuscript, we present an innovative approach to address nonlinear Bratu's problem
by applying the Discontinuous Galerkin method. Our method accurately computes two …

In this paper, we propose a method for solving some well-known classes of fractional Lane-
Emden type equations which are nonlinear ordinary differential equations on the semi …

In this work, the Nash equilibrium solution of nonlinear infinite-horizon nonzero-sum
differential games with open-loop information is investigated numerically. For this class of …

We extend the operational matrices technique to design a spectral solution of nonlinear
fractional differential equations (FDEs). The derivative is considered in the Caputo sense …

The paper is devoted to the study of operational matrix method for approximating solution for
nonlinear coupled system fractional differential equations. The main aim of this paper is to …

In this paper, we present a numerical scheme based on a modified form of shifted
Chebyshev polynomials to find the numerical solution of a class of fractional differential …

Purpose The main aim of the paper is to introduce the shifted fractional-order Gegenbauer
wavelets (SFGWs) and the development of a method for solving fractional nonlinear initial …