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 paper, a two-dimensional finite-difference technique for irregular meshes is formulated for derivatives up to the second order, where the domain in the vicinity of a given central point is broken into eight 45 degree pie shaped segments and the closest finite difference point in each segment to the center point is noted.
257 citations
TL;DR: Two finite-difference algorithms are presented for studying the dynamics of spatially extended predator–prey interactions with the Holling type II functional response and logistic growth of the prey and there are implementational advantages of the methods.
256 citations
TL;DR: In this paper, a framework for modeling coupled nucleation, growth and coarsening in diluted alloys is presented, based on the method of finite differences, where the particle distribution is divided into a series of discrete size classes, each represented by a control volume.
256 citations
Book•
18 Oct 2006
TL;DR: In this article, the reduction of Transient Heat Conduction Equations and Boundary Conditions and Substituting Heat-Conduction Equation by Two-Equations System are discussed.
Abstract: Heat Conduction Fundamentals.- Fourier Law.- Mass and Energy Balance Equations.- The Reduction of Transient Heat Conduction Equations and Boundary Conditions.- Substituting Heat Conduction Equation by Two-Equations System.- Variable Change.- Exercises. Solving Heat Conduction Problems.- Heat Transfer Fundamentals.- Two-Dimensional Steady-State Heat Conduction. Analytical Solutions.- Analytical Approximation Methods. Integral Heat Balance Method.- Two-Dimensional Steady-State Heat Conduction. Graphical Method.- Two-Dimensional Steady-State Problems. The Shape Coefficient.- Solving Steady-State Heat Conduction Problems by Means of Numerical Methods.- Finite Element Balance Method and Boundary Element Method.- Transient Heat Exchange between a Body with Lumped Thermal Capacity and Its Surroundings.- Transient Heat Conduction in Half-Space.- Transient Heat Conduction in Simple-Shape Elements.- Superposition Method in One-Dimensional Transient Heat Conduction Problems.- Transient Heat Conduction in a Semi-Infinite Body. The Inverse Problem.- Inverse Transient Heat Conduction Problems.- Multidimensional Problems. The Superposition Method.- Approximate Analytical Methods for Solving Transient Heat Conduction Problems.- Finite Difference Method.- Solving Transient Heat Conduction Problems by Means of Finite Element Method (FEM).- Numerical-Analytical Methods.- Solving Inverse Heat Conduction Problems by Means of Numerical Methods.- Heat Sources.- Melting and Solidification (Freezing).
255 citations
TL;DR: This paper first describes a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains, then turns its focus to the Stefan problem and constructs a third order accurate method that also includes an implicit time discretizations.
254 citations