Numerical bifurcation of separable parameterized equations.
Numerical blow-up for the -Laplacian equation with a nonlinear source
Numerical blow-up solutions for some semilinear heat equations.
Numerical boundary layers for hyperbolic systems in 1-D
The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.
Numerical boundary layers for hyperbolic systems in 1-D
The aim of this paper is to investigate the stability of boundary layers which appear in numerical solutions of hyperbolic systems of conservation laws in one space dimension on regular meshes. We prove stability under a size condition for Lax Friedrichs type schemes and inconditionnal stability in the scalar case. Examples of unstable boundary layers are also given.
Numerical Bounds for Inverses of Linear Operators
Numerical Calculation of Incomplete Gamma Functions by the Trapezoidal Rule.
Numerical calculation of the essential spectrum of a Laplacian.
Numerical calculations for some types of boundary value problems with unbounded domains
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Numerical computation of a nonlocal double obstacle problem.
Numerical computation of an analytic singular value decomposition of a matrix valued function.
Numerical Computation of Branch Points in Nonlinear Equations.
Numerical Computation of Branch Points in Ordinary Differential Equations.
Numerical Computation of Forced Oscillations in Coupled Duffing Equations.
Numerical Computation of Least Constants for the Sobolev Inequality.
Numerical Computation of Nonsimple Turning Points and Cusps.
Numerical computation of soliton dynamics for NLS equations in a driving potential.
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...