Higher-index differential-algebraic equations: analysis and numerical treatment
High-order methods for semilinear singularly perturbed boundary value problems.
Minimum principle for quadratic spline collocation discretization of a convection-diffusion problem
Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology
Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...
Nonstandard numerical methods for a class of predator-prey models with predator interference.
Numerical analysis of nonlinear model of excited carrier decay
This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved....
Numerical experiments with different schemes for a singularly perturbed problem.
Numerical modelling of a bridge subjected to simultaneous effect of a moving load and a vertical seismic ground excitation
A simple beam subjected to a row of regularly distributed moving forces and simultaneous vertical motions of its supports is described using a simplified theoretical model and a finite differences approach. Several levels of simplification of the structure and input data are supposed. Numerical results confirm legitimacy of the assumptions.
On a finite difference analogue of a singular boundary value problem.
On a finite difference analogue of forth order for boundary value problem.
On a fourth-order finite difference method for nonlinear two-point boundary value problems.
On collocation methods for singular perturbation problems of convection-diffusion type.
On difference schemes for quasilinear evolution problems.
On numerical solution of a mildly nonlinear turning point problem
On simulations of the classical harmonic oscillator equation by difference equations.
On the numerical solution of the diffusion equation with a nonlocal boundary condition.
On the Structure of Error Estimates for Finite-Difference Methods.
Opposing flows in a one dimensional convection-diffusion problem
In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...
Parameter-uniform fitted mesh method for singularly perturbed delay differential equations with layer behavior.
Robust monotone iterates for nonlinear singularly perturbed boundary value problems.