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: Numerical results demonstrate that the finite difference method for a Cauchy problem of generalized regularized long-wave (GRLW) equation is efficient and reliable.
97 citations
TL;DR: An efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models and produces an estimator with a lower variance than other methods, including the use of common random numbers, in most situations.
Abstract: We present an efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models. The estimator for the method is constructed by coupling the perturbed and nominal processes in a natural manner, and the analysis proceeds by utilizing a martingale representation for the coupled processes. The variance of the resulting estimator is shown to be an order of magnitude lower due to the coupling. We conclude that the proposed method produces an estimator with a lower variance than other methods, including the use of common random numbers, in most situations. Often the variance reduction is substantial. The method is no harder to implement than any standard continuous time Markov chain algorithm, such as “Gillespie's algorithm.” The motivating class of models, and the source of our examples, are the stochastic chemical kinetic models commonly used in the biosciences, though other natural application areas include population p...
97 citations
Book•
14 Sep 1987
TL;DR: In this paper, the Buckingham Pi Theorem Scaling was used to scale up the Buckingham pi scaling method for dimensionality analysis in the context of multidimensional analysis of continuous systems, and the Laplace Equation Hyperbolic Equations Index.
Abstract: DIMENSIONAL ANALYSIS AND SCALING: Dimensional Analysis The Buckingham Pi Theorem Scaling PERTURBATION METHODS: Regular Perturbation Singular Perturbation Boundary Layer Analysis Two Applications CALCULUS OF VARIATIONS: Variational Problems Necessary Conditions for Extrema The Simplest Problem Generalizations Hamiltonian Theory Isoperimetric Problems EQUATIONS OF APPLIED MATHEMATICS: Partial Differential Equations The Diffusion Equation Classical Techniques Integral Equations WAVE PHENOMENA IN CONTINUOUS SYSTEMS: Wave Propagation Mathematical Models of Continua The Wave Equation Gasdynamics Fluid Motions in R3 STABILITY AND BIFURCATION: Intuitive Ideas One Dimensional Problems Two Dimensional Problems Hydrodynamic Stability SIMILARITY METHODS Invariant Variational Problems Invariant Partial Differential Equations The General Similarity Method DIFFERENCE METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS: Finite Difference Methods The Diffusion Equation The Laplace Equation Hyperbolic Equations Index.
97 citations
TL;DR: VIM, established by He in (1999), is considered to solve nonlinear Bergur's equation and comparing the results with those of Adomian's decomposition and finite difference methods reveals significant points.
97 citations
TL;DR: A Galerkin finite element method with quadratic interpolation is employed in solving Poisson's equation to yield the electric potential solution in this article, and a backward difference method is utilized to compute the space charge density from the continuity equation.
Abstract: An accurate and efficient numerical scheme is presented for calculating electrical conditions inside wire‐duct electrostatic precipitators. A Galerkin finite‐element method with quadratic interpolation is employed in solving Poisson’s equation to yield the electric potential solution. A backward difference method is utilized to compute the space‐charge density from the continuity equation. The two methods are iteratively applied until convergence criteria for electric potential and current density are met. Computed potential and electric field values show good agreement with analytic solutions and experimental measurements. Comparisons between the present scheme and a finite‐difference scheme show that the finite‐element method offers distinct advantages in predicting the electrical characteristics of precipitators.
97 citations