In this paper, two new fourth-order derivative-free methods for finding multiple zeros of nonlinear equations are presented. In terms of computational cost the family requires three evaluations of functions per iteration. It is proved that the each of the methods has a convergence of order four. In this way it is demonstrated that the proposed class of methods supports the Kung-Traub hypothesis...

The purpose of this paper is to develop a numerical scheme for the two-dimensional fourth-order fractional subdiffusion equation with variable coefficients and delay. Using L2?1? approximation time Caputo derivative, finite difference method second-order accuracy in temporal direction achieved. novelty introduce problem under consideration coefficients, nonlinear source term, delay constant. re...

We propose and analyze a numerical method for solving fourth order differential equations modelling two point boundary value problems. The scheme is based on B-splines collocation. The error analysis is carried out and convergence rates are derived.

For a general class of methods, which includes linear multistep and RungeKutta methods as special cases, a concept of order relative to a given starting procedure is defined and an order of convergence theorem is proved. The definition is given an algebraic interpretation and illustrated by the derivation of a particular fourth-order method.

In this work, we have developed a fourth order Newton-like method based on harmonic mean and its multi-step version for solving system of nonlinear equations. The new fourth order method requires evaluation of one function and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each iteration. The proposed new scheme does not ...

We present a sixth order explicit compact finite difference scheme to solve the three dimensional (3D) convection diffusion equation. We first use multiscale multigrid method to solve the linear systems arising from a 19-point fourth order discretization scheme to compute the fourth order solutions on both the coarse grid and the fine grid. Then an operator based interpolation scheme combined w...

Abstract: In this paper, a comparison between h ig h e r order schemes has been performed in terms of numerical accuracy. Four finite difference schemes, the e xp lic it fourth-order compact Pade scheme, the implicit fourth-order Pade scheme, flowfield dependent variation (FDV) meth o d a n d h igh order compact flowfie ld dependent variation (HOC-FDV) scheme are tes ted. The FDV scheme is used...