We present new modifications to Newton’s method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to KungTraub’s conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical e...

quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the or...

The m-order connectivity index (G) m of a graph G is     1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i m d d d  G where 1 2 1 ... i i im d d d  runs over all paths of length m in G and i d denotes the degree of vertex i v . Also,        1 2 1 1 2 1 ... ... 1 ( ) i i im m v v v i i i ms d d d X G is its m-sum connectivity index. A dendrimer is an artificially manufactured or synth...

In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is ...

The construction of optimal fourth-order iterative schemes for solving univariate nonlinear equations is discussed. Per iteration, the methods consist of three evaluations of the function and they are free from any derivative calculation which property is so fruitful in engineering problems. We analytically show the fourth-order convergence. Numerical examples are considered to confirm the appl...

Abstract: In this study, the non-polynomial spline function is used to find the numerical solution of the third order singularly perturbed boundary value problems. The convergence analysis is discussed and the method is shown to have second order convergence. The order of convergence is improved up to fourth order using the improved end conditions. Numerical results are given to describe the ef...

The numerical solution of the Helmholtz equation with nonlocal radiation boundary conditions is considered. We model sound wave propagation in a multilayered piecewise homogeneous medium. A fourth-order accurate collocated, boundary element method is used, where the solution inside the domain is computed through a representation integral. The method is shown to have the expected fourth-order co...

In this paper, we present and analyse fourth order method for finding simultaneously multiple zeros of polynomial equations. S. M. Ilič and L. Rančič modified cubically convergent Ehrlich Aberth method to fourth order for the simultaneous determination of simple zeros [5]. We generalize this method to the case of multiple zeros of complex polynomial equations. It is proved that the method has f...