Differential Algebraic Equations (DAEs) are a general and implicit form of differential equations. DAEs are often used to represent physical systems such as dynamics of solids or chemical interactions. These equations are different from Ordinary Differential Equations (ODEs) in the sense that some of the dependent variables occur without their derivatives. Validated simulation of ODEs has recen...

This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, ea...

Composition is a powerful and simple approach for obtaining numerical integration methods of high accuracy order while preserving the geometric properties basic integrator. Adaptive step size control allows one to significantly increase performance methods. However, there lack efficient algorithms composition solvers due some known difficulties in constructing low-cost embedded local error esti...

In this paper, we introduce the new class of implicit L-stable generalized hybrid methods for the numerical solution of first order initial value problems. We generalize the hybrid methods with utilize ynv directly in the right hand side of classical hybrid methods. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the n...

In this paper we consider the numerical solution of 2D systems of certain types of taxis-diiusion-reaction equations from mathematical biology. By spatial discretization these PDE systems are approximated by systems of positive, nonlinear ODEs (Method of Lines). The aim of this paper is to examine the numerical integration of these ODE systems for low to moderate accuracy by means of splitting ...

Particle systems have been widely employed to animate deformable objects. In order to achieve real time capable systems often simplifications have been made to reduce the computational costs for solving the ODE at the expense of numerical and physical correctness. Implicit-Explicit (IMEX) methods provide a way to solve partly stiff systems efficiently, if the system meets some requirements. The...