Natural Runge-Kutta and Projection Methods.
Necessary conditions for the convergence of the generalized periodic overimplicit multistep method
This paper is the continuation of the paper "Generalized periodic overimplicit multistep methods" of the same author and it deals with the necessary and, in some special cases, with the necessary and sufficient conditions for the convergence of general periodic overimplicit multistep methods.
Nine-stage Multi-derivative Runge-Kutta method of order 12
Nonstandard numerical integrations of a Lotka-Volterra system.
Nonstandard numerical methods for a class of predator-prey models with predator interference.
Norm Bounds for Rational Matrix Functions.
Numerical approximation of singular boundary value problems for a nonlinear differential equation
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 model of a pine in a wind
Steady-state nonlinear differential equations govering the stem curve of a wind-loaded pine are derived and solved numerically. Comparison is made between the results computed and the data from photographs of a pine stem during strong wind. The pine breaking is solved at the end.
Numerical optimization of parameters in systems of differential equations
We present results on the estimation of unknown parameters in systems of ordinary differential equations in order to fit the output of models to real data. The numerical method is based on the nonlinear least squares problem along with the solution of sensitivity equations corresponding to the differential equations. We will present the performance of the method on the problem of fitting the output of basic compartmental epidemic models to data from the Covid-19 epidemic. This allows us to draw...
Numerical Solution of Bifurcation Problems for Ordinary Differential Equations.
Numerical Solution of Delay Differential Equations by Uniform Corrections to an Implicit Runge-Kutta Method.
Numerical solution of differential-algebraic equations for constrained mechanical motion.
Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation.
Numerical Solution of Ordinary and Retarded Differential Equations with Discontinuous Derivatives.
Numerical Solution of Retarded Initial Value Problems: Local and Global Error and Stepsize Control.
Numerical solution of some iterative differential equation
Numerical solution of the Maxwell equations in time-varying media using Magnus expansion
For the Maxwell equations in time-dependent media only finite difference schemes with time-dependent conductivity are known. In this paper we present a numerical scheme based on the Magnus expansion and operator splitting that can handle time-dependent permeability and permittivity too. We demonstrate our results with numerical tests.
Numerical solutions of nonstandard first order initial value problems.