Sebastiano Boscarino

Error Analysis of IMEX Runge-Kutta Methods Derived from Differential-Algebraic Systems

In this paper we present an error analysis of the IMEX Runge-Kutta methods when applied to stiff problems containing a nonstiff term and a stiff term, characterized by a small stiffness parameter

On a Class of Uniformly Accurate IMEX Runge-Kutta Schemes and Applications to Hyperbolic Systems with Relaxation

\varepsilon

Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit

. In this analysis we expand the global error in powers of

Flux-Explicit IMEX Runge--Kutta Schemes for Hyperbolic to Parabolic Relaxation Problems

\varepsilon

High Order Semi-implicit Schemes for Time Dependent Partial Differential Equations

and show that the coefficients of the error are the global errors of the IMEX Runge-Kutta method applied to a differential-algebraic system. Interesting convergence results of these errors and of the remainder of the expansion allow us to determine sharp error bounds for stiff problems. As a representative example of stiff problems we have chosen the van der Pol equation. We illustrate that the theoretical prediction is confirmed by the numerical test. Specifically, an order reduction phenomenon is observed when the problem becomes increasingly stiff. In particular, making several assumptions, we try to improve global error estimates of several IMEX Runge-Kutta methods existing in the literature.

High-Order Asymptotic-Preserving Methods for Fully Nonlinear Relaxation Problems

In this paper we consider hyperbolic systems with relaxation in which the relaxation time

Linearly Implicit IMEX Runge--Kutta Methods for a Class of Degenerate Convection-Diffusion Problems

\varepsilon

On the asymptotic properties of IMEX Runge-Kutta schemes for hyperbolic balance laws

may vary from values of order one to very small values. When

All Mach Number Second Order Semi-implicit Scheme for the Euler Equations of Gas Dynamics

\varepsilon

Implicit-Explicit Integral Deferred Correction Methods for Stiff Problems

is very small, the relaxation term becomes very strong and highly stiff, and underresolved numerical schemes may produce spurious results. In such cases it is important to have schemes that work uniformly with respect to