Stiff delay differential equations are frequently utilized in practice, but their numerical simulations difficult due to the complicated interaction between stiff and terms. At moment, only a few low-order algorithms offer acceptable convergent stable features. Exponential integrators type of efficient approach for problems that can eliminate influence stiffness on scheme by precisely dealing w...

This lecture is a survey of the theory of stability and error bounds for numerical methods for stii initial value problems. We begin with problems in singular perturbation form, where the distinction between \fast" and \slow" variables is clearest. Next we explain Kreiss's characterization of stii problems that includes singular perturbation problems as a special case. The requirement of unifor...

In this paper, using the polynomial extrapolation, we solve an initial value problem in ordinary differential equations. The aim of this paper is to compare with the fourth-order Runge-Kutta method on the basis of accuracy for a given number of function evaluations.

We will consider the efficient implementation of a fourth order two stage implicit Runge-Kutta method to solve periodic second order initial value problems. To solve the resulting systems, we will use the factorization of the discretized operator. Such proposed factorization involves both complex and real arithmetic. The latter case is considered here. The resulting system will be efficient and...

We consider linear multistep methods that possess general monotonicity and boundedness properties. Strict monotonicity, in terms of arbitrary starting values for the multistep schemes, is only valid for a small class of methods, under very stringent step size restrictions. This makes them uncompetitive with the strong-stability-preserving (SSP) Runge– Kutta methods. By relaxing these strict mon...