On the occasion of 60 years to a seminal paper by the Swedish mathematician Germund
Dahlquist, this review paper starts by discussing the celebrated Dahlquist's barriers, which …

Implicit block methods for solving initial value problems in ordinary differential equations are
well-known among the contemporary scientific community, since they are cost-effective, self …

In this paper, an efficient fourth-derivative two-step hybrid block strategy (FDTHBS) to get the
approximate solution of a third-order IVP with applications to problems in Fluid Dynamics …

This study aims to develop, analyze and implement an efficient method for approximating
two-point boundary value problems of ordinary differential equations. The method contains …

In this paper, we develop an optimized hybrid block method which is combined with a
modified cubic B-spline method, for solving non-linear partial differential equations. In …

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 …

In the past decades, many applications related to applied physics, physiology and
astrophysics have been modelled using a class of two-point singular boundary value …

This study presents a new variant of the hybrid block methods (HBMs) for solving initial
value problems (IVPs). The overlapping hybrid block technique is developed by changing …

This paper presents the construction and implementation of a three-step optimized hybrid
method for solving stiff system of first order initial value problems of ordinary differential …

The second derivative block hybrid method for the continuous integration of differential
systems within the interval of integration was derived. The second derivative block hybrid …