Sharp estimates for the convergence of the density of the Euler scheme in small time.
Solving dynamical systems with cubic trigonometric splines.
Solving Linear Ordinary Differential Equations by Exponentials of Iterated Commutators.
Some applications of the Pascal matrix to the study of numerical methods for differential equations
In this paper we introduce and analyze some relations between the Pascal matrix and a new class of numerical methods for differential equations obtained generalizing the Adams methods. In particular, we shall prove that these methods are suitable for solving stiff problems since their absolute stability regions contain the negative half complex plane.
Some remarks on the intervals of stability of Runge-Kutta methods after Richardson extrapolation
Spline collocation methods for solving second order neutral delay differential equations.
Spline solution of some linear boundary value problems.
Split Linear Multistep Methods for the Numerical Integration of Stiff Differential Systems.
Stability analysis of a difference scheme for the vibration equation with a finite number of degrees of freedom
Stability analysis of linear multistep methods for delay differential equations.
Stability analysis of numerical methods for delay differential equations.
Stability Analysis of One-Step Methods for Neutral Delay-Differential Equations.
Stability and Accuracy of Time Discretizations for Initial Value Problems
Stability and B-Convergence of Linearly Implicit Runge-Kutta Methods.
Stability of Explicit Time Discretizations for Solving Initial Value Problems.
Stability of Explicit Time Discretizations for Solving Initial Value Problems.
Stability of the method of lines.
Stability of the Multistep-Methods on Variable Grids.
Stability properties of differential-algebraic equations and Spin-stabilized discretizations.
Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems
The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh,...