An Algebraic Characterization of B-convergent Runge-Kutta Methods.
An algebraic theory of order
In this paper, we present an abstract framework which describes algebraically the derivation of order conditions independently of the nature of differential equations considered or the type of integrators used to solve them. Our structure includes a Hopf algebra of functions, whose properties are used to answer several questions of prime interest in numerical analysis. In particular, we show that, under some mild assumptions, there exist integrators of arbitrarily high orders for arbitrary (modified)...
An algorithm for determining the number of linearly independent comitants of a system of differential equations
An algorithm for model reduction in large electric power systems.
An algorithm for the numerical solution of differential equations of fractional order.
An Analysis and Improvement of the El~mistikawy and Werle Scheme
An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations
We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...
An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations
We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...
An analytic proof of numerical stability of Gaussian collocation for delay differential
In questo articolo si investigano le proprietà di stabilità asintotica dei metodi numerici per equazioni differenziali con ritardo, prendendo in esame l'equazione test: dove , , e è una funzione a valori reali e continua. In particolare, viene analizzata la dipendenza dal ritardo della stabilità numerica dei metodi di collocazione Gaussiana. Nel recente lavoro [GH99], la stabilità di questi metodi è stata dimostrata facendo uso di un approccio geometrico, basato sul legame tra la proprietà...
An Approximation Theorem for Second-Order Evolution Equations.
An efficient generalization of the Rush--Larsen method for solving electro-physiology membrane equations.
An efficient zero-stable numerical method for fourth-order differential equations.
An exponentially fitted method for singularly perturbed delay differential equations.
An Extension of the ...2 Procedure.
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time...
An Iteration Method for Studying the Bifurcation of Solutions of the Nonlinear Equations, L(...) u + ..R (..., u) = 0 .
An Iteration Scheme for Boundary Value-Alternative Problems.
An iterative method of solving differential equations
An ODE-Solver Based on the Method of Averaging.