Fast local convergence with single and multistep methods for nonlinear equations

Local convergence analysis of tensor methods for nonlinear equations

Local Convergence of Adaptive Methods for Nonlinear Partial Differential Equations

In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and then use the theory to obtain convergence results for practical adaptive finite element methods (AFEM) applied to several classes of nonlinear elliptic equations. In the first part of the paper, we develop a weak-* convergence fra...

New iterative methods with seventh-order convergence for solving nonlinear equations

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.

‎Multistep collocation method for nonlinear delay integral equations

‎The main purpose of this paper is to study the numerical solution of nonlinear Volterra integral equations with constant delays, based on the multistep collocation method. These methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. Also, we analyze the convergence of the...

Implicit-explicit multistep methods for nonlinear parabolic equations

Implicit–explicit multistep methods for nonlinear parabolic equations were recently analyzed in [2, 3, 1]. In these papers the linear operator of the equation is assumed time-independent, self-adjoint and positive definite; then, the linear part is discretized implicitly and the remaining part explicitly. Here we slightly relax the hypotheses on the linear operator by allowing part of it to be ...