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...

The effect of formaldehyde on kinetics of biomass growth and consump­ tion of glucose by yeasts Candida tropicalis CC Y 29-7-33 has been inves­ tigated. For modelling of kinetics of biomass growth and consumption of the substrate the models according to Monod, Contois, and Andrews were applied. The parameters of kinetic equations were determined using the combined explicit and implicit Euler me...

We propose a novel approach for the numerical integration of diffusion-type equations with variable and degenerate mobility or diffusion coefficient. Our focus is the Cahn-Hilliard equation which plays a prominent role in phase field models of fluids and soft materials but the methodology has a more general applicability. The central idea is a split method with a linearly implicit component and...

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

In this paper we study the convergence of the semi-implicit and the implicit Euler methods for the time integration of abstract, quasilinear hyperbolic evolution equations. The analytical framework considered here includes certain quasilinear Maxwell’s and wave equations as special cases. Our analysis shows that the Euler approximations are well-posed and convergent of order one. The techniques...

In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(OD...

This paper presents a case study of numerical simulations in an easy-to-use matrix computation framework named Simple Interface for Library Collections (SILC), which allows users to use various matrix computation libraries in an environmentand language-independent manner. As a practical example of numerical simulations in SILC, we selected cloth simulation based on a mass-spring model and the i...

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically-rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation h...

We derive a new model for seawater intrusion phenomena in free aquifers. It combines the efficiency of the sharp interface approach with the physical realism of the diffuse interface one. More precisely, a phase field is used as an intermediate variable for including the exchanges between the characteristic layers of the aquifer (salt water, fresh water, unsaturated zone). The threedimensional ...