This manuscript presents a one-step method incorporating a second-derivative applied to
obtain approximate solutions of first-order initial-value problems of ordinary and time …

In this paper, the implementation of second derivative general linear methods (SGLMs) in a
variable stepsize environment using Nordsieck technique is discussed and various …

Backward differential formulae (BDF) are the basis of the highly efficient schemes for the
numerical solution of stiff ordinary differential equations for decades. An alternative multistep …

This work introduces a new one-step method with three intermediate points for solving stiff
differential systems. These types of problems appear in different disciplines and, in …

Explicit general linear method of two-step peer-type of order 1 to 4 suitable for solving non-
stiff ordinary differential equations are derived. Estimates of the local truncation error are …

We describe some issues related to the development of a new code for numerical solution of
systems of Volterra integral equations of the second kind. This code is based on A-and V 0 …

We introduce multivalue second derivative collocation methods for the numerical solution of
stiff ordinary differential equations, also arising from the spatial discretization of time …

Contrary to the implementation of multistep (or multivalue) methods based on Nordsieck
technique, variable stepsize (VS) methods do not require updating the input quantities when …

General linear methods (GLMs) are a large family of methods which have been already
introduced for the numerical solution of Volterra integral equations of the second kind. In this …

The paper deals with the construction of explicit Nordsieck second derivative general linear
methods with s stages of order p with and high stage order with inherent Runge–Kutta or …