Numerical aspects of computation of periodic and quasiperiodic solutions in systems of partial differential equations
Numerical bifurcation and stability analysis of the Nicolis-Puhl reaction as an application of a class of integro-partial differential equations.
Numerical calculations for some types of boundary value problems with unbounded domains
Numerical Computation of Branch Points in Ordinary Differential Equations.
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...
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 k of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large k are large nonlinear exponents σ. In a second part, we compute...
Numerical computation of the eigenvalues for the spheroidal wave equation with accurate error estimation by matrix method.
Numerical Error Bounds for Fourth Order Boundary Value Problems, Simultaneous Estimation of u(x) and u"(x).
Numerical experiments with different schemes for a singularly perturbed problem.
Numerical imperfections near a critical point
Numerical methods for approximating eigenvalues of boundary value problems.
Numerical modelling and simulation of liquid-impelled loop reactor.
Numerical modelling of tube fixing in the heat exchanger of a nuclear power plant
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. ...
Numerical schemes for multivalued backward stochastic differential systems
We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational...
Numerical Solution of Bifurcation Problems for Ordinary Differential Equations.
Numerical solution of boundary value problems by least squares
Numerical solution of boundary value problems for selfadjoint differential equations of th order
The paper is devoted to solving boundary value problems for self-adjoint linear differential equations of th order in the case that the corresponding differential operator is self-adjoint and positive semidefinite. The method proposed consists in transforming the original problem to solving several initial value problems for certain systems of first order ODEs. Even if this approach may be used for quite general linear boundary value problems, the new algorithms described here exploit the special...
Numerical Solution of Delay Differential Equations by Uniform Corrections to an Implicit Runge-Kutta Method.