摘要:

AbstractTheoretical proofs state that the planar Winslow or homogenous Thompson–Thames–Mastin (hTTM) map is a diffeomorphism, yet numerical solutions to the hTTM equations produce folded grids on the so‐called “horseshoe” domain. A quasi‐analytic solution to the horseshoe problem is constructed to demonstrate that folding is due to truncation error effects. Higher‐order difference methods are also explored. © 1995 John W

ISSN:0749-159X    

DOI:10.1002/num.1690110603

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractA method that combines computer science and numerical analysis techniques for the solution of elliptic partial differential equations in domains consisting of the union of rectangles is presented. It is applied to Laplace's equation and to the Navier–Stokes equations in several domains. The method is very flexible and can be easily modified to solve other equations. © 1995 John Wiley&Sons, I

ISSN:0749-159X    

DOI:10.1002/num.1690110604

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractIn this article we study a finite‐difference system, which is a discrete version of a class of nonlinear reaction‐diffusion systems with time delays. Existence‐comparison and uniqueness theorem are first established for the discretized problem by the method of upper and lower solutions. A monotone iterative scheme is also developed for the solution of the finite‐difference system. Under a convergence acceleration scheme, it is shown that the monotone sequences converge quadratically to the solution of the finite‐difference system. At last, numerical results on some model problems are demonstrated to substantiate our theorems. © 1995 John Wiley

ISSN:0749-159X    

DOI:10.1002/num.1690110605

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractA new front tracking method based on grid deformation is combined with a streamline upwind Petrov–Galerkin finite element method to produce an adaptive method for application to convection‐dominated transport equations. In this work, we examine the practicality of this approach and demonstrate the method on one‐dimensional examples. © 1995 John Wiley&Son

ISSN:0749-159X    

DOI:10.1002/num.1690110606

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractA second‐order‐accurate and unconditionally stable operator‐splitting algorithm for the three‐dimensional diffusion equation is presented in this article. The governing equation is split into three one‐dimensional equations, and the split equations are solved by a finite‐element method. The simulation characteristics of the algorithm are demonstrated by numerical experiments. © 1995 John Wil

ISSN:0749-159X    

DOI:10.1002/num.1690110607

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

摘要:

AbstractIn the implicit formulation of the transversal method of lines, numerical instabilities (singular perturbation) do occur whenever “small” step sizes of the discretized variable have to be used for some reason. This problem can effectively be avoided if the derivatives with respect to the discretized variable are chosen using a combination of implicit and explicit methods (the biplicit method). This combination method uses piecewise defined trial functions involving a certain number of free parameters. The values of these parameters are found by the requirement that the trial functions approximate the solution of the implicit formulation of the method of lines. From a mathematical point of view, this spectral‐collocation‐type ansatz results in a multipoint boundary‐value problem with added parameters to be determined. Two numerical examples are presented in order to illustrate the performance of the method. © 1995 John Wiley

ISSN:0749-159X    

DOI:10.1002/num.1690110608

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690110602

出版商:John Wiley&Sons, Inc.    

年代:1995

数据来源: WILEY