On convergence of the projective integration method for stiff ordinary differential equations

On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations

We present a convergence proof for higher order implementations of the projective integration method (PI) for a class of deterministic multi-scale systems in which fast variables quickly settle on a slow manifold. The error is shown to contain contributions associated with the length of the microsolver, the numerical accuracy of the macrosolver and the distance from the slow manifold caused by ...

On Convergence of the Projective Integration Method for Stiff Ordinary Differential Equations

Abstract. We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to center manifold theory. The error is shown to contain contributions associated with the numerical accuracy of the microsolver, the numerical accuracy of the macrosolver and the distance from the center manifold caused by the combi...

Convergence of the multistage variational iteration method for solving a general system of ordinary differential equations

In this paper, the multistage variational iteration method is implemented to solve a general form of the system of first-order differential equations. The convergence of the proposed method is given. To illustrate the proposed method, it is applied to a model for HIV infection of CD4+ T cells and the numerical results are compared with those of a recently proposed method.

Integration of Partitioned Stiff Systems of Ordinary Differential Equations

Abstract. Partitioned systems of ordinary differential equations are in qualitative terms characterized as monotonically max-norm stable if each sub-system is stable and if the couplings from one sub-system to the others are weak. Each sub-system of the partitioned system may be discretized independently by the backward Euler formula using solution values from the other sub-systems correspondin...

A quasi-interpolation method for solving stiff ordinary differential equations