In contrast to stiff deterministic systems of ordinary differential equations, in general, the implicit Euler method for stiff stochastic differential equations is not effective. This paper introduces a new numerical method for stiff differential equations which consists of interlacing large implicit Euler time steps with a sequence of small explicit Euler time steps. We emphasize that uniform ...

Two midpoint-trapezoid pairs of dynamically equivalent (conjugate) algorithms are derived as compositions of first-order forward Euler and backward Euler integrators as applied to an incremental form of the initial-value problem of three-dimensional rigid body rotation. The algorithms are related to the recently developed methodology of the so-called Munthe-Kaas Runge–Kutta methods. Selected ex...

In this paper, two different numerical schemes, namely the Runge-Kutta fourth order method and the implicit Euler method with perturbation method of the second degree, are applied to solve the nonlinear thermal wave in one and two dimensions using the differential quadrature method. The aim of this paper is to make comparison between previous numerical schemes and detect which is more efficient...

We show that a mechanical model of a pin-jointed linked structure is exactly equivalent to a symplectic Euler discretisation of a Hamiltonian ODE system. The step-size of this discretisation relates to a mechanical quantity which can take arbitrary values. Thus we may explore the behaviour of the symplectic Euler method in regions not normally considered appropriate for a numerical scheme and i...

We discuss the numerical solution of differential equations of fractional order with discontinuous right–hand side. Problems of this kind arise, for instance, in sliding mode control. After applying a set–valued regularization, the behavior of some generalizations of the implicit Euler method is investigated. We show that the scheme in the family of fractional Adams methods possesses the same c...

An error bound is proved for a fully practical piecewise linear nite element approximation, using a backward Euler time discretization, of the Cahn-Hilliard equation with a logarithmic free energy.

In this work, we establish the maximal [Formula: see text]-regularity for several time stepping schemes for a fractional evolution model, which involves a fractional derivative of order [Formula: see text], [Formula: see text], in time. These schemes include convolution quadratures generated by backward Euler method and second-order backward difference formula, the L1 scheme, explicit Euler met...