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Tikhonov, A.N. and Samarskii, A.A. (2011) Equations of Mathematical Physics. Dover Publishers, New York.

has been cited by the following article:

• TITLE: A New Analysis of an Implicit Mimetic Scheme for the Heat Equation

  AUTHORS: Mariela Castillo Nava, Juan Manuel Guevara-Jordan

  KEYWORDS: Mimetic, Finite Difference, Robin’s Condition, Implicit, Stable, Transient, Heat

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.3, March 31, 2023

  ABSTRACT: A mimetic finite difference scheme for the transient heat equation under Robin’s conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate the space derivatives. The temporal derivative is replaced by a first order backward difference approximation to obtain an implicit formulation. The resulting scheme contains nonstandard finite difference stencils. An original convergence analysis by the matrix’s method shows that the proposed scheme is unconditionally stable. A comparative study against standard finite difference schemes, based on central difference or first order one side approximations, reveals the advantages of our scheme without being its implementation more expensive or difficult to achieve.