Generalized Fourier Transform Method for Solving Nonlinear Anomalous Diffusion Equations

Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations

Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this me...

Nonlinear Integrable Equations and Nonlinear Fourier Transform

In this paper we study nonlocal functionals whose kernels are homogeneous generalized functions. We also use such functionals to solve the Kortewegde Vries (KdV), the nonlinear Schrödinger (NLS) and the Davey-Stewartson (DS) equations. The solution of certain integrable equations in terms of formal power series was obtained in [4], [5]. In these papers the solution was expressed in a formal pow...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

On the Generalized Halley Method for Solving Nonlinear Equations

Halley’s method is a famous iteration method for solving nonlinear equations F (X) = 0. Some Kantorovich-like theorems have been given, including extensions for general spaces. Quasi-Halley methods were proposed too. This paper uses the generalized inverse approach in order to obtain a robust generalized Halley method.

A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS

In this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. Periteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the eighth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new ...