Two point fully implicit block method of variable step size is developed for solving directly the second order system of Ordinary Differential Equations (ODEs). This method will estimate the solutions of Initial Value Problems (IVPs) at two points simultaneously. The method developed is suitable for the numerical integration of non stiff and mildly stiff differential systems. Numerical results ...

A new numerical integration code (COLDDAE) for general linear differentialalgebraic equations (DDAEs) of retarded and neutral type is discussed. The implementation is based on the regularization technique introduced in [13]. In the single delay case, the code can handle noncausal systems, i.e., systems, where the solution at the current time does not only depend on the system at the past and cu...

Through introducing a new iterative formula for divided difference using Neville's and Aitken's algorithms, we study new iterative methods for interpolation, numerical differentiation and numerical integration formulas with arbitrary order of accuracy for evenly or unevenly spaced data. Basic computer algorithms for new methods are given.

The proper application of a shadow model during the integration of orbit trajectories requires that the solar radiation pressure be sampled adequately during transitions between lighting conditions. An integration scheme is presented in which the lighting condition is held constant across steps of a primary integrator. If the lighting condition changes during that step, then an Encke-like integ...

A new conservative numerical integration algorithm for the integrable Henon–Heiles system is presented which conserves all of the constants of motion.

A generalization of two sharp inequalities in a recent paper by N. Ujević is established. Applications in numerical integration are also given and the results of N. Ujević are revised and improved. c © 2006 Elsevier Ltd. All rights reserved.

The anhamtonic effective pair potentials ~(u)=au~~+~u~/3!+yu~/4! in K& and CsBr have been investigated at room temperature by the EXAFS technique. In the parameter fitting, we have directly carried out the numerical integration of EXAFS function and evaluated the anharmonic effective pair potential. The Griineisen parameters y, were calculated from the obtained values of a and 6 as 1.65 for KBr...

Highly-oscillatory integrals are allegedly difficult to calculate. The main assertion of this paper is that that impression is incorrect. As long as appropriate quadrature methods are used, their accuracy increases when oscillation becomes faster and suitable choice of quadrature points renders this welcome phenomenon more pronounced. We focus our analysis on Filon-type quadrature and analyse i...