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Finite Difference Method

Numerical Methods for Atmospheric and Oceanic Sciences, 2016
The chapter discusses the mathematical description of transport, diffusion, and wave phenomena and their numerical simulation with finite difference methods. The accuracy of the methods is investigated via stability and consistency properties assuming the existence of regular solutions.
S. Bartels
openaire   +3 more sources

Mimetic finite difference method [PDF]

open access: possibleJournal of Computational Physics, 2014
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus.
K Lipnikov, G Manzini, M Shashkov
openaire   +3 more sources

Dynamics and bifurcations of a discrete‐time Lotka–Volterra model using nonstandard finite difference discretization method

Mathematical methods in the applied sciences, 2022
A newly disclosed nonstandard finite difference method has been used to discretize a Lotka–Volterra model to investigate the critical normal form coefficients of bifurcations for both one‐parameter and two‐parameter bifurcations.
Z. Eskandari   +3 more
semanticscholar   +1 more source

Finite Difference Methods [PDF]

open access: possible, 1996
As was mentioned in Chap. 1, all conservation equations have similar structure and may be regarded as special cases of a generic transport equation, Eq. (1.26), (1.27) or (1.28). For this reason, we shall treat only a single, generic conservation equation in this and the following chapters.
Milovan Perić, Joel H. Ferziger
openaire   +1 more source

Finite Difference Methods

2018
This chapter offers a peek at the vast literature on numerical methods for partial differential equations. The focus is on finite difference methods (FDM): approximating differential operators by functions of difference operators. Padé approximants (Fornberg) give a unifying principle for deriving the various stencils used by numericists.
Thiago Carvalho Peixoto   +2 more
  +6 more sources

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