In this paper, we introduce a method to solve linear stiff IVPs. The suggested method, which we call modified homotopy perturbation method, can be considered as an extension of the homotopy perturbation method (HPM) which is very efficient in solving a varety of differential and algebraic equations. In this work, a class of linear stiff initial value problems (IVPs) are solved by the classical ...

When performing dynamic analysis of a constrained mechanical system, a set of index three differential-algebraic equations (DAE) describes the time evolution of the system. The paper presents a state space based method for the numerical solution of the resulting DAE. A subset of so-called independent generalized coordinates, equal in number to the number of degrees of freedom of the mechanical ...

An improved stabilized multilevel Monte Carlo (MLMC) method is introduced for stiff stochastic differential equations in the mean square sense. Using S-ROCK2 with weak order 2 on the finest time grid and S-ROCK1 (weak order 1) on the other levels reduces the bias while preserving all the stability features of the stabilized MLMC approach. Numerical experiments illustrate the theoretical findings.

This paper introduces some implicitness in stochastic terms of numerical methods for solving stiff stochastic differential equations and especially a class of fully implicit methods, the balanced methods. Their order of strong convergence is proved. Numerical experiments compare the stability properties of these schemes with explicit ones.

This paper deals with the stability of Runge–Kutta methods for a class of stiff systems of nonlinear Volterra delay-integro-differential equations. Two classes of methods are considered: Runge–Kutta methods extended with a compound quadrature rule, and Runge– Kutta methods extended with a Pouzet type quadrature technique. Global and asymptotic stability criteria for both types of methods are de...

In this paper, we present a class of explicit numerical methods for stiff Itô stochastic differential equations (SDEs). These methods are as simple to program and to use as the well-known Euler-Maruyama method, but much more efficient for stiff SDEs. For such problems, it is well known that standard explicit methods face step-size reduction. While semi-implicit methods can avoid these problems ...

A class of explicit linear multistep methods is suggested as basic methods for the CDS schemes introduced in [3]. These schemes are designed for the numerical solution of certain stiff ordinary differential equations, and operate with dominant eigenvalues, and the corresponding eigenvectors, of the Jacobian. The motivation, and the stability analysis for CDS schemes assumes that the eigensystem...

The Generalized Backward Differentiation methods for solving stiff higher-order ordinary differential equations are described. The convergence, zero stability and consistency of these methods are defined. Next, the zero stability and consistency conditions necessary for convergence are proven. The order for which the methods are zero stable is also determined.

In this paper, new integration methods for stiff ordinary differential equations (ODEs) are developed. Following the idea of quantization–based integration (QBI), i.e., replacing the time discretization by state quantization, the proposed algorithms generalize the idea of linearly implicit algorithms. Also, the implementation of the new algorithms in a DEVS simulation tool is discussed. The eff...

We consider inital-value problems governed by a system of autonomous ordinary differential equations (ODEs). When the required integration stepsize of the ODE system is very very small in comparison to the time domain of interest. Then the initial-value problem is said to be stiff.