In this paper we consider a new fourth-order method of BDF-type for solving stiff initial-value problems, based on the interval approximation of the true solution by truncated Chebyshev series. It is shown that the method may be formulated in an equivalent way as a Runge–Kutta method having stage order four. Themethod thus obtained have good properties relatives to stability including an unboun...

An error analysis of Runge-Kutta convolution quadrature is presented for a class of nonsectorial operators whose Laplace transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ0 and a polynomial bound O(s 1) there, the stronger polynomial bound O(s2) in convex sectors of the form | arg s| ≤ π/2 − θ < π/2 for θ > 0. The order of convergence of the Runge-Kutt...

In this article, a new Runge-Kutta-Nyström method is derived. The new RKN method has zero phase-lag, zero amplification error and zero first derivative of phase-lag. This method is basically based on the sixth algebraic order Runge-Kutta-Nyström method, which has proposed by Dormand, El-Mikkawy and Prince. Numerical illustrations show that the new proposed method is much efficient as compared w...

When one solves differential equations, modeling physical phenomena, it is of great importance to take physical constraints into account. More precisely, numerical schemes have to be designed such that discrete solutions satisfy the same constraints as exact solutions. Based on general theory for positivity, with an explicit third-order Runge-Kutta method (we will refer to it as RK3 method) pos...

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.