The monodomain model is widely used in in-silico cardiology to describe excitation propagation the myocardium. Frequently, operator splitting decouple stiff reaction term and diffusion so that they can be solved separately. Commonly, implicitly with a large time step while by using an explicit method adaptive stepping. In this work, we propose fully for solution of decoupled model. contrast sem...

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

Simulation of soft tissue behavior for surgical training systems is a particularly demanding application of deformable modeling. Explicit integration methods on single mesh require small time step to maintain stability, but this produces slow convergence spatially through the object. In this paper, we propose a multigrid integration scheme to improve the stability and convergence of explicit in...

In the recent years, there has been an increasing interest in discontinuous Galerkin time domain (DGTD) methods for the solution of the unsteady Maxwell equations modeling electromagnetic wave propagation. One of the main features of DGTD methods is their ability to deal with unstructured meshes which are particularly well suited to the discretization of the geometrical details and heterogeneou...

Efficiency of numerical integration methods for a biologically detailed neuron model is examined. Because of the wide range of time constants, neuron equations are considered stiff. Stiffness is a property of a system in which the time step required to maintain stability for an explicit method is much smaller than the time step required to achieve a desired level of accuracy. Traditional explic...

The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way with respect to the computational cost o...

This paper revisits the Taylor method for the numerical integration of initial value problems of Ordinary Differential Equations (ODEs). The main goal is to show that the Taylor method can be competitive, both in speed and accuracy, with the standard methods. To this end, we present a computer program that outputs an specific numerical integrator for a given set of ODEs. The generated code incl...

A computationally efficient method for discrete modelling of cracks in laminated composite structures using explicit time integration is proposed. Discrete crack involves formation strong discontinuities and the domain elements must be transformed to include this discontinuity. In integration, results a reduction stable increment an analysis corresponding increase computational cost limits its ...