The purpose of this paper is to give a numerical treatment for a class of nonlinear multipoint boundary value problems. The multipoint boundary condition under consideration includes various commonly discussed boundary conditions, such as the threeor four-point boundary condition. The problems are discretized by the fourth-order Numerov’s method. The existence and uniqueness of the numerical so...

A class of three-pointmethods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski’s fourth-ordermethods and amodified Newton’s method in the third step, obtained by a suitable approximation of the first derivative using the product of three weight functions. The proposed three-step methods have order eight costing only fou...

In this paper, we present a new iterative method with order of convergence sixth for solving nonlinear equations. This method is developed by extending a fourth order method of Ostrowski. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the sixth order of convergence is given. Several numerical ex...

We present a derivative free method of fourth order convergence for solving systems of nonlinear equations. The method consists of two steps of which first step is the well-known Traub’s method. First-order divided difference operator for functions of several variables and direct computation by Taylor’s expansion are used to prove the local convergence order. Computational efficiency of new met...

Higher-order finite-volume methods have been shown to be more efficient than secondorder methods. However no consensus has been reached on how to eliminating the oscillations caused by solution discontinuities. Essentially non-oscillatory (ENO) schemes provide a solution but are computationally expensive to implement and may not converge well for steady-state problems. This work studies the app...

The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...

We present a fourth-order compact finite difference scheme on the face centered cubic (FCC) grids for the numerical solution of the two-dimensional convection diffusion equation. The seven-point formula is defined on a regular hexagon, where the strategy of directional derivative is employed to make the derivation procedure straightforward, efficient, and concise. A corresponding multigrid meth...

In this work, we propose a new fourth-order Jarratt-type method for solving systems of nonlinear equations. The local convergence order of the method is proven analytically. Finally, we validate our results via some numerical experiments including an application to the Chandrashekar integral equations.

We develop a family of fourth-order iterative methods using the weighted harmonic mean of two derivative functions to compute approximatemultiple roots of nonlinear equations.They are proved to be optimally convergent in the sense of Kung-Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the develo...

We prove some new results which justify the use of interval truncation as a means of regularising a singular fourth order Sturm-Liouville problem near a singular endpoint. Of particular interest are the results in the so called lim-3 case, which has no analogue in second order singular problems.