Convergence of the time-discretized monotonic schemes

Julien Salomon

Displaying similar documents to “Convergence of the time-discretized monotonic schemes”

Convergence of a high-order compact finite difference scheme for a nonlinear Black–Scholes equation

Bertram Düring, Michel Fournié, Ansgar Jüngel (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides. ...

Discrete dynamic programming and viscosity solutions of the Bellman equation

I. Capuzzo Dolcetta, M. Falcone (1989)

Annales de l'I.H.P. Analyse non linéaire

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Finite volume schemes for the p-laplacian on cartesian meshes

Boris Andreianov, Franck Boyer, Florence Hubert (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible,...

Adaptive step-size control in simulation of diffusive CVD processes.

Geiser, Jürgen, Fleck, Christian (2009)

Mathematical Problems in Engineering

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Convergence of a mimetic finite difference method for static diffusion equation.

Guevara-Jordan, J.M., Rojas, S., Freites-Villegas, M., Castillo, J.E. (2007)

Advances in Difference Equations [electronic only]

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A new conservative finite difference scheme for Boussinesq paradigm equation

Natalia Kolkovska, Milena Dimova (2012)

Open Mathematics

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A family of nonlinear conservative finite difference schemes for the multidimensional Boussinesq Paradigm Equation is considered. A second order of convergence and a preservation of the discrete energy for this approach are proved. Existence and boundedness of the discrete solution on an appropriate time interval are established. The schemes have been numerically tested on the models of the propagation of a soliton and the interaction of two solitons. The numerical experiments demonstrate...

On the convergence of a three-level vector SOR scheme.

Jovanović, B.S. (1995)

Matematichki Vesnik

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On the convergence of min/sup points in optimal control problems.

Bagh, Adib (2001)

Abstract and Applied Analysis

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Non linear schemes for the heat equation in 1D

Bruno Després (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Inspired by the growing use of non linear discretization techniques for the linear diffusion equation in industrial codes, we construct and analyze various explicit non linear finite volume schemes for the heat equation in dimension one. These schemes are inspired by the Le Potier’s trick [348 (2010) 691–695]. They preserve the maximum principle and admit a finite volume formulation. We provide a original functional setting for the analysis of convergence of such methods. In particular...