We present a local convergence analysis of a Modified Halley-Like Method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet-derivative [26]. Numerical examples are also ...

in this paper, we investigate the goursat problem in the class c21(d)cn0 (d  p) c00 (d q)for a third order pseudoparabolic equation. some results are given concerning the existence and uniquenessfor the solution of the suggested problem.

We present a study of the influence of different approximation schemes on the convergence rate of volume rendering integral (VRI) numerical approximations. We experimentally evaluate the impact of numerical integration techniques on the rate of convergence to the correct solution of the VRI on a single ray. We report that the discretization of both the inner and outer integrals have influence o...

In this paper, a published algorithm is investigated that proposes a three-step iterative method for solving nonlinear equations. This method is considered to be efficient with third order of convergence and an improvement to previous methods. This paper proves that the order of convergence of the previous scheme is two, and the efficiency index is less than the corresponding Newton’s method. I...