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 iterative method of solving differential equations
An ODE-Solver Based on the Method of Averaging.
Analysis of lumped parameter models for blood flow simulations and their relation with 1D models
This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee...
Analysis of lumped parameter models for blood flow simulations and their relation with 1D models
This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that...
Analysis of the linearly implicit mid-point rule for differential- algebraic equations.
Application of analytic continuation to approximate solution of differential equation
Application of differential equations for transforming the implicit functions into the explicit ones
Application of Hermitian Splines to the Initial Value Problem
Applications numériques de la dualité en mécanique hamiltonienne
Approximate solutions of matrix differential equations.
A method for solving second order matrix differential equations avoiding the increase of the dimension of the problem is presented. Explicit approximate solutions and an error bound of them in terms of data are given.
Approximation by circular splines for solutions of ordinary differential equations
Approximation theorem for evolution operators
This paper is devoted to the study of the approximation problem for the abstract hyperbolic differential equation u'(t) = A(t)u(t) for t ∈ [0,T], where A(t):t ∈ [0,T] is a family of closed linear operators, without assuming the density of their domains.
A-priori Error Estimates of Galerkin Backward Differentiation Methods in Time-Inhomogeneous Parabolic Problem.
A-stable block implicit methods containing second derivatives
Asymptotic Bounds on the Errors of One-Step Methods.
Asymptotic Error Expansions for Stiff Equations: an Analysis for the Implicit Midpoint and Trapezoidal Rules in the Strongly Stiff Case.
Asymptotic Expansions of the Global Error of Fixed-Stepsize Methods.