This paper reviews various aspects of stiffness in the numerical solution of initial-value
problems for systems of ordinary differential equations. In the literature on numerical …

Abstract Both Runge-Kutta and linear multistep methods are available to solve initial value
problems for ordinary differential equations in the R packages deSolve and deTestSet …

Symplecticity is also an important property for exponential Runge–Kutta (ERK) methods in
the sense of structure preservation once the underlying problem is a Hamiltonian system …

In the numerical solution of ODEs by implicit time-stepping methods, a system of (nonlinear)
equations has to be solved each step. It is common practice to use fixed-point iterations or …

In this paper we investigate local convergence properties of inexact Newton and Newton-
like methods for systems of nonlinear equations. Processes with modified relative residual …

Using the Becker-Döring cluster equations as an example, we highlight some of the
problems that can arise in the numerical approximation of dynamical systems with slowly …

This article proposes an algorithm for express solutions in nonlinear structural dynamics.
Our strategy is to adopt a typical time integrator and accept the solution after a constant …

This paper studies the stability and convergence properties of general Runge-Kutta methods
when they are applied to stiff semilinear systems y′(t)= J (t) y (t)+ g (t, y (t)) with the stiffness …

The convergence properties of a newly defined uniparametric family of collocation Runge–
Kutta methods on non-stiff systems, stiff semi-linear problems and Differential-Algebraic …

This paper is concerned with the development of the Newton-arithmetic mean method for
large systems of nonlinear equations with block-partitioned Jacobian matrix. This method is …