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: The newly proposed method is based on the Hopf–Cole transformation, which transforms the original nonlinear Burgers’ equation into a linear heat equation, and transforms the Dirichlet boundary condition into the Robin boundary condition, which leads to an implicit fourth-order compact finite difference scheme.
116 citations
TL;DR: The mimetic finite difference method introduced by Hyman and Shashkov is exploited to present a framework for estimating vector fields and related scalar fields (divergence, curl) of physical interest from image sequences to provide a basis for consistent definitions of higher-order differential operators.
Abstract: We exploit the mimetic finite difference method introduced by Hyman and Shashkov to present a framework for estimating vector fields and related scalar fields (divergence, curl) of physical interest from image sequences. Our approach provides a basis for consistent definitions of higher-order differential operators, for the analysis and a novel stability result concerning second-order div-curl regularizers, for novel variational schemes to the estimation of solenoidal (divergence-free) image flows, and to convergent numerical methods in terms of subspace corrections.
116 citations
TL;DR: In this paper, a method for computing the modes of dielectric guiding structures based on finite differences is described, and the numerical computation program is efficient and can be applied to a wide range of problems.
Abstract: A method for computing the modes of dielectric guiding structures based on finite differences is described. The numerical computation program is efficient and can be applied to a wide range of problems. We report here solutions for circular and rectangular dielectric waveguides and compare our solutions with those obtained by other methods. Limitations in the commonly used approximate formulas developed by Marcatili are discussed.
116 citations
TL;DR: In this article, the magnitude of the current at a plane electrode in a rectangular channel under conditions of steady state, fully developed laminar flow is numerically computed based on the backward implicit finite difference numerical method, applied to solve the differential equation governing convective diffusion.
116 citations
TL;DR: In this paper, the authors considered a generalization of the classical vibrating string problem in the following respects: a) the motion is two dimensional, b) large displacements are permitted, forces due to the weight of the cable, buoyancy, drag and virtual inertia of the medium are included, and d) the properties of a cable need not be uniform.
Abstract: The system of nonlinear partial differential equations governing the transient motion of a cable immersed in a fluid is solved by finite difference methods. This problem may be considered a generalization of the classical vibrating string problem in the following respects: a) the motion is two dimensional, b) large displacements are permitted, c) forces due to the weight of the cable, buoyancy, drag and virtual inertia of the medium are included, and d) the properties of the cable need not be uniform. The numerical solution of this system of equations presents a number of interesting mathematical problems related to: a) the nonlinear nature of the equations, b) the determination of a stable numerical procedure, and c) the determination of an effective computational method. The solution of this problem is of practical significance in the calculation of the transient forces acting on mooring and towing lines which are subjected to arbitrarily prescribed motions. 1. Introduction. This problem arose as a result of an urgent requirement by the Navy in connection with a series of nuclear explosion tests which were conducted in the Pacific. In preparation for these tests a number of ships were instrumented and moored at specified locations from the explosion point. These positions had to be maintained intact during the period preceding the explosion. However, the bobbing up and down of the ships due to ocean waves could excite transient forces in the mooring lines sufficient to break them and thus result in the loss of informa- tion from the tests. Several months prior to these tests a request was made to the Applied Mathematics Laboratory to calculate the magnitude of the forces acting on the mooring lines for waves of varying amplitude and frequency. The two factors which made a theoretical solution feasible at this time, whereas it would not have been possible several years ago, 'vere: a) the availability of a high-speed computer and b) the recent progress made in the understanding and development of nu- merical methods for the solution of systems of partial differential equations by finite-difference methods. Although this problem was solved to satisfy a specific request, it is more useful to regard it as the general problem of the two-dimensional motion of a cable or rope immersed in a fluid, and it becomes immediately apparent that its solution i.s applicable to a wide class of engineering problems involving the motion of cables. such as: a) the laying of submarine telegraph cables, b) the towing of a ship or other object in water, or c) the snapping of power lines as a result of transient forces caused by storms. The problem may be stated abstractly as follows: Given the initial conditions (i.e., position and velocity at any time, t0) and boundary
116 citations