Stabilized or Chebyshev explicit methods have been widely used in the past to solve stiff ordinary differential equations. Making use of special properties of Chebyshev-like polynomials, these methods have favorable stability properties compared to standard explicit methods while remaining explicit. A new class of such methods, called ROCK, introduced in [Numer. Math., 90, 1-18, 2001] has recen...

Abstract—Existing Block Backward Differentiation Formulae (BBDF) of different orders are collected based on their competency and accuracy in solving stiff ordinary differential equations (ODEs). The strategy to fully utilize the formulae is optimized using variable step variable order approach. The improved performances in terms of accuracy and computation time are presented in the numerical re...

In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for t...

Application of the Haar wavelet approach for solving stiff differential equations is discussed. Solution of singular perturbation problems is also considered. Efficiency of the recommended method is demonstrated by means of four numerical examples, mostly taken from well-known textbooks.

Extrapolation methods using the structure in the equations of motion of multibody systems are given in this article. The methods are explicit in the differential part and implicit in the nonlinear constraints. They admit a robust formulation in which only linear systems of equations are solved most of the time. Related methods, which are linearly implicit also in the differential part, are deve...

This article presents two regularization techniques for systems of state-dependent neutral delay differential equations which have a discontinuity in the derivative of the solution at the initial point. Such problems have a rich dynamics and besides classical solutions can have weak solutions in the sense of Utkin. Both of the presented techniques permit the numerical solution of such problems ...

Abstract: In this paper, we present a class of multistep methods for the numerical solution of stiff ordinary differential equations. In these methods the first, second and third derivatives of the solution are used to improve the accuracy and absolute stability regions of the methods. The constructed methods are A-stable up to order 6 and A(α)-stable up to order 8 so that, as it is shown in th...

The numerical solution of boundary value problems for certain stiff ordinary differential equations is studied. The methods developed use singular perturbation theory to construct approximate numerical solutions which are valid asymptotically; hence, they have the desirable feature of becoming more accurate as the equations become stiffer. Several numerical examples are presented which demonstr...

Radial basis function-Pseudospectral method and Fourier Pseudospectral (FPS) method are extended for stiff nonlinear partial differential equations with a particular emphasis on the comparison of the two methods. Fourth-order Runge-Kutta scheme is applied for temporal discretization. The numerical results indicate that RBF-PS method can be more accurate than standard Fourier pseudospectral meth...

This paper describes the development of a four-point fully implicit block method for solving first order ordinary differential equations (ODEs) using variable step size. This method will estimate the solutions of initial value problems (IVPs) at four points simultaneously. The method developed is suitable for the numerical integration of non-stiff and mildly stiff differential systems. The perf...