DRP scheme optimization
A new DRP scheme is built, which enables us to minimize the error due to the finite difference approximation, by means of an equivalent matrix equation.
math.AP↗
arXiv subjects
Claire David
Publications and source records attributed to Claire David.
Finite Difference Schemes as a Matrix Equation
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
math.AP↗
Theoretical Optimization of Finite Difference Schemes
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the numerical error is taken into account. The theoretical study of a related linear algebraic problem gives general results which can lead to the determination of the optimal scheme.
math.AP↗
Spurious solitons and structural stability of finite difference schemes for nonlinear wave equations
The goal of this work is to determine classes of traveling Solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.
math.AP↗
A Note On 3Solitary Wave Solutions of the Compound Burgers-Korteweg-de Vries Equation"
The goal of this note is to construct a class of traveling solitary wave solutions for the compound Burgers-Korteweg-de Vries equation by means of a hyperbolic ansatz.
math.AP↗
A linear dispersive mechanism for numerical error growth: spurious caustics
A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity. Several popular schemes are analyzed and are shown to admit spurious caustics. It is also observed that caustic-free schemes can be defined, like the Crank-Nicolson scheme.
math.AP↗