Modification of Newtons method with higher-order convergence is presented. The modification of Newtons method is based on Frontinis three-order method. The new method requires two-step per iteration. Analysis of convergence demonstrates that the order of convergence is 6. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newtons method and ...

Using the original two-step iteration process, we develop a conservative finitedifference scheme for the problem of femtosecond pulse propagation in semiconductor under the action of an external electric field. Its advantages consist in its applicability for the problem with non-uniform boundary conditions and it possesses also a property of asymptotic stability. Therefore, it is possible to pr...

This paper will concentrate on contributions of CWI to the development of parallel Runge-Kutta (RK) methods. We shall describe two approaches to construct such methods. In both approaches, a conventional implicit RK method is used as a corrector equation whose solution is approximated by an iterative method. In the first approach, the iteration method uses a fixed number of iterations without s...

Existence and uniqueness are established for a translation-invariant Gibbs measure corresponding to a spatial point process that has, in addition to inhibition and clustering, the new feature of penalizing isolated points. It is shown that this point process has the so-called two-step Markov property, and a theorem is proved that characterizes the more general m-step Markov density functions. T...

We study the numerical behavior of stationary one-step or two-step matrix splitting iteration methods for solving large sparse systems of linear equations. We show that inexact solutions of inner linear systems associated with the matrix splittings may considerably influence the accuracy of the approximate solutions computed in finite precision arithmetic. For a general stationary matrix splitt...

this paper presents a hybrid technique for simultaneous estimation of parameter and function in inverse heat conduction problems. no prior information is used for the functional form of the heat flux in the present study. the scheme presented here is a combination of two different classical methods: the variable metric method (vmm) and gauss method (gm). the determination of the unknown thermal...

In this paper, we introduce a new parameter iteration method (P-Iteration for short) ,which can be applied on Adams-Moulton methods to solve initial value problems. Compared with Jacobi iteration method, it has three advantages: (1) it may significantly implement the stable region of the iterative process such that we can efficiently use the large stable region of implicit formula; (2) it allow...