This book deals with numerical methods for solving partial differential equa tions (PDEs)
coupling advection, diffusion and reaction terms, with a focus on time-dependency. A …

Over the past 40 years, the speed of computers has increased roughly by one order of
magnitude per decade. During the next decade, continuing progress, particularly in parallel …

The derivation of low-storage, explicit Runge–Kutta (ERK) schemes has been performed in
the context of integrating the compressible Navier–Stokes equations via direct numerical …

A semi-implicit formulation of the method of spectral deferred corrections (SISDC) for
ordinary differential equations with both stiff and non-stiff terms is presented. Several …

Summary The Runge-Kutta-Chebyshev method is an s-stage Runge-Kutta method designed
for the explicit integration of stiff systems of ordinary differential equations originating from …

A key issue in developing efficient numerical schemes for nonlinear wave equations is the
energy-conserving. Most existing schemes of the energy-conserving are fully implicit and the …

In this note we present a new Rosenbrock solver which is third-order accurate for nonlinear
parabolic problems. Since Rosenbrock methods suffer from order reduction when they are …

In the recent paper by Dutt, Greengard and Rokhlin, a variant of deferred or defect correction
methods is presented which couples Gaussian quadrature with the Picard integral equation …

We derive a new class of parallelizable two-step peer methods for the numerical solution of
stiff systems of Ordinary Differential Equations (ODEs), inspired by a technique introduced in …

A semi-implicit form of spectral deferred corrections is used in a method of lines approach to
create a projection method that is sixth-order accurate in both time and space for simple …