Book Chapter10.1007/978-1-4471-4075-7_4
Finite Difference Methods for Partial Differential Equations
Jakob Andreas Bærentzen,Jens Gravesen,François Anton,Henrik Aanæs +3 more
- 01 Jan 2012
- pp 65-79
51
TL;DR: In this article, the authors give an introduction to methods for computing derivatives and partial derivatives using discrete differential operators and discuss the connection to Taylor series, and give an overview of the Taylor series.
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Abstract: In this chapter, we initially give an introduction to methods for computing derivatives and partial derivatives using discrete differential operators and discuss the connection to Taylor series.
read more
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Citations
A survey of sparse matrix research
Iain S. Duff
- 01 Apr 1977
TL;DR: This paper surveys the state of the art in sparse matrix research in January 1976, and discusses the solution of sparse simultaneous linear equations, including the storage of such matrices and the effect of paging on sparse matrix algorithms.
278
Electron trajectory program
W.B. Herrmannsfeldt
- 01 Nov 1979
TL;DR: The SLAC Electron Trajectory Program as mentioned in this paper is a program specifically written to compute trajectories of charged particles in electrostatic and magnetostatic focusing systems including the effects of space charge and self-magnetic fields.
On the use of nonstandard finite difference methods
TL;DR: In this survey article, the author tries to provide as much stimulating information as available regarding these NSFDMs to the researchers, which will be helpful for them as the research proceeds in this direction.
154
Parameter identification in distributed systems: A synthesizing overview
Michael P. Polis,R. E. Goodson +1 more
- 01 Jan 1976
TL;DR: In this paper, the distributed system parameter identification problem can be treated as a series of largely independent subproblems, each of which must be considered in any attempt to treat the problem in applications.
125
Electromagnetic pulse scattering in time-varying inhomogeneous media
TL;DR: In this article, a finite difference solution technique is used to solve Maxwell's equations directly in the treatment of electromagnetic pulse scattering in a time-varying inhomogeneous medium, where axial symmetry is obtained.
120
References
•Book
Level Set Methods and Dynamic Implicit Surfaces
Stanley Osher,Ronald Fedkiw +1 more
- 31 Oct 2002
TL;DR: A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.
6.1K
•Book
Numerical methods for conservation laws
Randall J. LeVeque
- 01 Jan 1990
TL;DR: In this paper, the authors describe the derivation of conservation laws and apply them to linear systems, including the linear advection equation, the Euler equation, and the Riemann problem.
4.2K
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Numerical solution of partial differential equations : finite difference methods
Gordon Dennis Smith
- 01 Jan 1978
TL;DR: In this article, the standard finite difference methods of parabolic, hyperbolic, and elliptic equations are discussed, together with the concomitant theoretical work on consistency, stability, and convergence.
2.3K
Numerical Solution of Partial Differential Equations: An Introduction
K. W. Morton,David Francis Mayers +1 more
- 01 Apr 2005
TL;DR: In this paper, the authors provide a concise introduction to standard numerical techniques, ones chosen on the basis of their general utility for practical problems, including finite difference methods for simple examples of parabolic, hyperbolic and elliptic equations.
899