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 …

We study the construction of explicit second derivative general linear methods (SGLMs) with
strong stability preserving (SSP) property which are designed for the numerical solution of …

We describe an approach to global error estimation for explicit general linear methods. This
approach is based on computation of two numerical solutions by pairs of general linear …

In this work, we present a novel class of high-order time integrators for the numerical
solution of ordinary differential equations. These integrators are of the two-derivative type, ie …

In this manuscript, we propose a new family of stabilized explicit parallelizable peer methods
for the solution of stiff Initial Value Problems (IVPs). These methods are derived through the …

When faced with the task of solving stiff problems, highly stable numerical methods are often
needed to avoid the phenomenon of order reduction. The purpose of this paper is to …

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

Time stepping methods are often required for solving system of ordinary differential
equations arising from spatial discretization of partial differential equations. In our prior work …

When faced with the task of solving hyperbolic partial differential equations (PDEs), high
order, strong stability-preserving (SSP) time integration methods are often needed to ensure …