Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: This paper shows that very accurate solutions can be achieved using the optimal value of the constant shape parameter in PDE problems solved with a multiquadric based RBF finite difference (RBF-FD) method.
112 citations
Book•
01 Jun 1987
TL;DR: In this paper, the FEBS method is used to study the stability of boundary-value problems for Equations of Second Order and First and Second Order Difference Equations, respectively.
Abstract: Ordinary Difference Equations. Difference Equations of First and Second Order. Examples of Difference Schemes. Boundary-Value Problems for Equations of Second Order. Basis of the FEBS Method. Difference Schemes for Ordinary Differential Equations. Elementary Examples of Difference Schemes. Convergence of the Solutions of Difference Equations as a Consequence of Approximation and Stability. Widely-Used Difference Schemes. Difference Schemes for Partial Differential Equations. Basic Concepts. Simplest Examples of the Construction and Study of Difference Schemes. Some Basic Methods for the Study of Stability. Difference Scheme Concepts in the Computation of Generalized Solutions. Problems with Two Space Variable. The Concept of Difference Schemes with Splitting. Elliptic Problems. Concept of Variational-Difference and Projection-Difference Schemes. Stability of Evolutional Boundary-Value Problems Viewed as the Boundedness of Norms of Powers of a Certain Operator. Construction of the Transition Operator. Spectral Criterion for the Stability of Nonselfadjoint Evolutional Boundary-Value Problems. Appendix: Method of Internal Boundary Conditions. Bibliographical Commentaries. Bibliography. Index.
112 citations
TL;DR: This work presents an algorithm for computing a set of intervals to be used in a forward-difference approximation of the gradient, and shows how certain “standard” choices for the finite-Difference interval may lead to poor derivative approximations for badly scaled problems.
Abstract: When minimizing a smooth nonlinear function whose derivatives are not available, a popular approach is to use a gradient method with a finite-difference approximation substituted for the exact gradient In order for such a method to be effective, it must be possible to compute “good” derivative approximations without requiring a large number of function evaluations Certain “standard” choices for the finite-difference interval may lead to poor derivative approximations for badly scaled problems We present an algorithm for computing a set of intervals to be used in a forward-difference approximation of the gradient
112 citations
TL;DR: In this paper, a numerical study of the thermal transport process has been carried out, assuming a two-dimensional steady circumstance, and the boundary layer equations, as well as full governing equations including buoyancey effects, are solved employing finite difference techniques.
Abstract: The heat transfer arising due to the movement of a continuous heated plate in processes such as hot rolling and hot extrusion has been studied. Of particular interest were the resulting temperature distribution in the solid and the proper imposition of the boundary conditions at the location where the material emerges from a furnace or die. These considerations are important in the simulation and design of practical systems. A numerical study of the thermal transport process has been carried out, assuming a two-dimensional steady circumstance. The boundary layer equations, as well as full governing equations including buoyancey effects, are solved employing finite difference techniques. The effect of various physical parameters, which determine the temperature and flow fields, is studied in detail. The significance of these results in actual manufacturing processes is discussed.
112 citations
TL;DR: In this paper, the authors proposed a simple method that eliminates both problems and results in a fast, robust procedure that uses less computation time for the same level of prediction accuracy when compared to other finite-difference schemes.
112 citations