Stiff hyperbolic balance laws exhibit large spectral gaps, especially if the relaxation term significantly varies in space. Using examples from rarefied gases and general form of underlying law model, we perform a detailed analysis semi-discrete model that reveals gaps. Based on that, show inefficiency standard time integration schemes expressed by severe restriction CFL number. We then develop...

Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of underlying differential equation system cannot belong to class general methods. This poses a major challenge for stability analysis such since new iterate depends nonlinearly on current iterate. Moreover, systems, existence is always associated with zero eigenvalues, so steady states cont...

We introduce ABC-schemes, a new class of linearly implicit one-step methods for numerical integration of stiff ordinary differential equation systems. Formulas of ABC-schemes invoke the Jacobian of differential system similary to the methods of Rosenbrock type, but unlike the latter they include also the square of the Jacobian matrix.

1 Abstract. This paper examines a class of explicit nite-diierence advection schemes derived along the method of lines. An important application eld is large-scale atmospheric transport. The paper therefore focuses on the demand of positivity. For the spatial discretization, attention is connned to conservative schemes using 5 points per direction. The 4-th order central scheme and the family o...

A first order accurate fully implicit integration scheme and four different explicit substepping schemes with automatic error control are used in this paper to integrate the constitutive relations of a critical state model for saturated soils. Their respective computational performance terms accuracy efficiency is assessed provide practical guidance deciding which five most suitable solving num...

In this work, we propose Runge-Kutta time integration schemes for the incompressible Navier-Stokes equations with two salient properties. First, velocity and pressure computations are segregated at the time integration level, without the need to perform additional fractional step techniques that spoil high orders of accuracy. Second, the proposed methods keep the same order of accuracy for both...