Nine-stage Multi-derivative Runge-Kutta method of order 12
Numerical precision for differential inclusions with uniqueness
In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is in general and when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl’s rheological model, our estimates in maximum norm do not depend on spatial dimension.
Numerical precision for differential inclusions with uniqueness
In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is 1/2 in general and 1 when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl's rheological model, our estimates in maximum norm do not depend on spatial dimension. ...
On a fourth-order finite difference method for nonlinear two-point boundary value problems.
On order 5 symplectic explicit Runge-Kutta Nyström methods.
On Orthogonal Series Solution For Boundary Layer Problems
On the comparison of error bounds for finite difference schemes.
On the convergence of multistep methods for nonlinear stiff differential equations.
On the convergence of multistep methods for nonlinear two-point boundary value problems
On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods.
On the Structure of Error Estimates for Finite-Difference Methods.
One-step methods for ordinary differential equations with parameters
In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.
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...
Optimale Runge-Kutta-Verfahren der Ordnung 2 und 3.
Phase portraits of planar vector fields: Computer proofs.
Propagation of errors in dynamic iterative schemes
We consider iterative schemes applied to systems of linear ordinary differential equations and investigate their convergence in terms of magnitudes of the coefficients given in the systems. We address the question of whether the reordering of equations in a given system improves the convergence of an iterative scheme.
Regularity and approximability of the solutions to the chemical master equation
The chemical master equation is a fundamental equation in chemical kinetics. It underlies the classical reaction-rate equations and takes stochastic effects into account. In this paper we give a simple argument showing that the solutions of a large class of chemical master equations are bounded in weighted ℓ1-spaces and possess high-order moments. This class includes all equations in which no reactions between two or more already present molecules and further external reactants occur that add mass...
Schranken für die Norm der Greenschen Funktion gewöhnlicher Differentialoperatoren.
Solving dynamical systems with cubic trigonometric splines.
Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.