Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
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TL;DR: In this article, the authors derived a second-order difference approximation for the Riemann-Liouville fractional derivative in spatial space, and analyzed the solvability, conditional stability and convergence of the proposed scheme by using the Fourier method.
100 citations
TL;DR: In this article, the Richardson extrapolation technique is extended to time-dependent problems and applied to the Lax-Wendroff and Crank-Nicholson finite difference schemes which are used to approximate solutions to the convection-diffusion equation.
Abstract: The technique of Richardson extrapolation, which has previously been used on time-independent problems, is extended so that it can also be used on time-dependent problems. The technique presented is completed in the sense that the extrapolated solution is calculated at all spatial grid nodes which coincide with nodes of the finest grid considered. Numerical examples are presented when the technique is applied to the Lax–Wendroff and Crank–Nicholson finite difference schemes which are used to approximate solutions to the convection–diffusion equation. The examples show that extrapolation can be an easy and efficient way in which to produce accurate numerical solutions to time-dependent problems. © 1997 John Wiley & Sons, Ltd.
99 citations
99 citations
TL;DR: In this article, a finite difference method was applied to the analysis of the temporal and spatial stability of the three-dimensional boundary layer flow on a swept wing, and the results showed that the algorithm can be reduced significantly by exploiting the special structure of two matrices.
Abstract: The present investigation is concerned with a fourth order accurate finite difference method and its application to the study of the temporal and spatial stability of the three-dimensional compressible boundary layer flow on a swept wing. This method belongs to the class of compact two-point difference schemes discussed by White (1974) and Keller (1974). The method was apparently first used for solving the two-dimensional boundary layer equations. Attention is given to the governing equations, the solution technique, and the search for eigenvalues. A general purpose subroutine is employed for solving a block tridiagonal system of equations. The computer time can be reduced significantly by exploiting the special structure of two matrices.
99 citations
TL;DR: The finite element method, using smooth splines as basis functions, applied to the model problem $u_t = cu_x $ with periodic data generates a differential-difference equation whose phase error is closely estimated and compared with the phase error of both explicit and high order implicit centered differencing as mentioned in this paper.
Abstract: The finite element method, using smooth splines as basis functions, applied to the model problem $u_t = cu_x $ with periodic data generates a differential-difference equation whose phase error is closely estimated and compared with the phase error of both explicit and high order implicit centered differencing. We also compute and compare the minimum work required to obtain a fixed error for several fully discrete schemes.
99 citations