Displaying similar documents to “Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis”

Implicit difference schemes for mixed problems related to parabolic functional differential equations

Milena Netka (2011)

Annales Polonici Mathematici

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Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.

Comparison of explicit and implicit difference schemes for parabolic functional differential equations

Zdzisław Kamont, Karolina Kropielnicka (2012)

Annales Polonici Mathematici

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Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both...

Difference methods for parabolic functional differential problems of the Neumann type

K. Kropielnicka (2007)

Annales Polonici Mathematici

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Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given...

Convergent semidiscretization of a nonlinear fourth order parabolic system

Ansgar Jüngel, René Pinnau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential. Exploiting the stability of the discretization, convergence is shown in the multi-dimensional case. Under some assumptions on the regularity of the solution, the rate of convergence proves to be optimal.

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

Bertram Düring, Michel Fournié, Ansgar Jüngel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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. ...

A new compact finite difference quasilinearization method for nonlinear evolution partial differential equations

P.G. Dlamini, M. Khumalo (2017)

Open Mathematics

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This article presents a new method of solving partial differential equations. The method is an improvement of the previously reported compact finite difference quasilinearization method (CFDQLM) which is a combination of compact finite difference schemes and quasilinearization techniques. Previous applications of compact finite difference (FD) schemes when solving parabolic partial differential equations has been solely on discretizing the spatial variables and another numerical technique...