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Finite-difference and finite-element methods of approximation
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1971Abstract The finite-difference and finite-element methods for approximating the solution of elliptic boundary-value problems are discussed. The analysis of the order of accuracy is outlined, and the results compared, with some comment on special problems connected with singularities.
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1995
Finite-difference methods are important for two reasons. First, they form the background to almost all later developments. Secondly, a finite-difference method is relatively easy to construct and program to solve a particular problem, or class of problems, that may not be suitable for an existing general purpose software package using, say, finite ...
Richard L. Stoll, Kazimierz Zakrzewski
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Finite-difference methods are important for two reasons. First, they form the background to almost all later developments. Secondly, a finite-difference method is relatively easy to construct and program to solve a particular problem, or class of problems, that may not be suitable for an existing general purpose software package using, say, finite ...
Richard L. Stoll, Kazimierz Zakrzewski
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1969
With the aid of electronic computers we can easily calculate the behaviour of oscillating water in even the most complex surge tank systems by using finite difference methods. Consequently these methods are of great importance.
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With the aid of electronic computers we can easily calculate the behaviour of oscillating water in even the most complex surge tank systems by using finite difference methods. Consequently these methods are of great importance.
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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.
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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.
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2001
The finite difference method is a universally applicable numerical method for the solution of differential equations. In this chapter, for a sample parabolic partial differential equation, we introduce some difference schemes and analyze their convergence. We present the well-known Lax equivalence theorem and related theoretical results, and apply them
Kendall Atkinson, Weimin Han
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The finite difference method is a universally applicable numerical method for the solution of differential equations. In this chapter, for a sample parabolic partial differential equation, we introduce some difference schemes and analyze their convergence. We present the well-known Lax equivalence theorem and related theoretical results, and apply them
Kendall Atkinson, Weimin Han
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2010
Illustrate the concept of the finite difference method for the simple one dimensional case of solute diffusion, with and without advective transport, for both stationary and non stationary cases. Generalize the concept of the finite difference method for two and three dimensional geometries.
Michel Rappaz +2 more
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Illustrate the concept of the finite difference method for the simple one dimensional case of solute diffusion, with and without advective transport, for both stationary and non stationary cases. Generalize the concept of the finite difference method for two and three dimensional geometries.
Michel Rappaz +2 more
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1999
The finite difference method was traditionally used in electron optics for solving field distributions. Even for magnetic field calculations, where the finite element method has largely replaced it, there are instances where the finite difference method is still advocated [1]. Finite elements are closely related to finite differences, indeed, there are
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The finite difference method was traditionally used in electron optics for solving field distributions. Even for magnetic field calculations, where the finite element method has largely replaced it, there are instances where the finite difference method is still advocated [1]. Finite elements are closely related to finite differences, indeed, there are
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A generalization of the method of finite differences
Information Processing Letters, 1973D. Holnapy, Miklós Szöts, A. Botár
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