scholarly journals On exponential fitting of finite difference methods for heat equations

2021 ◽  
pp. 1-12
Author(s):  
E.O. Tuggen ◽  
C.E. Abhulimen
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Truncation Error ◽  
Finite Difference Methods ◽  
Exponential Fitting ◽  
Heat Equations ◽  
Local Truncation Error ◽  
Difference Methods ◽  
Exponentially Fitted ◽  
Diffusion Problems

Abstract In this article, a new kind of finite difference scheme that is exponentially fitted, inspired from Fourier analysis, for a fourth space derivative was developed for solving diffusion problems. Dispersion relation and local truncation error of the method were discussed. Stability analysis of the method revealed that it is conditionally stable. Compared to the corresponding fourth order classical scheme in the literature, the proposed scheme is efficient and accurate. Mathematics Subject Classification (2020): 65M06, 65N06. Keywords: Exponential fitting, Finite difference, Local truncation error, Heat equations.

A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES

2005 ◽  
Vol 15 (10) ◽  
pp. 1533-1551 ◽  
Author(s):  
FRANCO BREZZI ◽  
KONSTANTIN LIPNIKOV ◽  
VALERIA SIMONCINI
Keyword(s):  
Finite Difference ◽  
Material Properties ◽  
Numerical Experiments ◽  
Finite Difference Methods ◽  
Polyhedral Meshes ◽  
Discretization Schemes ◽  
Difference Methods ◽  
Theoretical Results ◽  
Diffusion Problems

A family of inexpensive discretization schemes for diffusion problems on unstructured polygonal and polyhedral meshes is introduced. The material properties are described by a full tensor. The theoretical results are confirmed with numerical experiments.

NUMERICAL INTERFACES IN FINITE DIFFERENCE METHODS FOR HYPERBOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

1993 ◽  
Vol 01 (02) ◽  
pp. 151-184 ◽  
Author(s):  
TAO LIN
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Convergence Rates ◽  
Hyperbolic Equations ◽  
Finite Difference Methods ◽  
Discontinuous Coefficients ◽  
Interface Problems ◽  
Artificial Boundary ◽  
Numerical Examples ◽  
Difference Methods

In this paper, we discuss the interface problems arising in using finite difference methods to solve hyperbolic equations with discontinuous coefficients. The schemes developed here can be used to handle four important types of numerical interfaces due to: (1) the discontinuity of the coefficients of the PDE, (2) using artificial boundary, (3) using different finite difference formulae in different areas, and (4) using different grid sizes in different areas. Stability analysis for these schemes is carried out in terms of conventional l1, l2, and l∞ norms so that the convergence rates of these schemes are obtained. Several numerical examples are supplied to demonstrate properties of these schemes.

scholarly journals Numerical Solutions of the Modified Burgers’ Equation by Finite Difference Methods

2017 ◽  
Vol 13 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Yusuf Ucar ◽  
Nuri Murat Yagmurlu ◽  
Orkun Tasbozan
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Finite Difference Methods ◽  
Solution Process ◽  
Modified Burgers Equation ◽  
Finite Difference Equations ◽  
Difference Methods ◽  
Linearization Techniques

Abstract In this study, a numerical solution of the modified Burgers’ equation is obtained by the finite difference methods. For the solution process, two linearization techniques have been applied to get over the non-linear term existing in the equation. Then, some comparisons have been made between the obtained results and those available in the literature. Furthermore, the error norms L2 and L∞ are computed and found to be sufficiently small and compatible with others in the literature. The stability analysis of the linearized finite difference equations obtained by two different linearization techniques has been separately conducted via Fourier stability analysis method.

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