摘要:

AbstractA variety of time‐linearization, quasilinearization, operator‐splitting, and implicit techniques which use compact or Hermitian operators has been developed for and applied to one‐dimensional reaction‐diffusion equations. Compact operators are compared with second‐order accurate spatial approximations in order to assess the accuracy and efficiency of Hermitian techniques. It is shown that time‐linearization, quasilinearization, and implicit techniques which use compact operators are less accurate than second‐order accurate spatial discretizations if first‐order approximations are employed to evaluate the time derivatives. This is attributed to first‐order accurati temporal truncation errors. Compact operator techniques which use second‐order temporal approximations are found to be more accurate and efficient than second‐order accurate, in both space and time, algorithms. Quasilinearization methods are found to be more accurate than time‐linearization schemes. However, quasilinearization techniques are less efficient because they require the inversion of block tridiagonal matrices at each iteration. Some improvements in accuracy can be obtained by using partial quasilinearization and linearizing each equation with respect to the variable whose equation is being solved. Operator‐splitting methods which use compact differences to evaluate the diffusion operator were found to be less accurate than operator‐splitting procedures employ second‐order accurate spatial approximations. Comparisons among the methods presented in this paper are shown in terms of the L2‐norm errors and computed wave speeds for a variety of time steps and grid spacings: The numerical efficiency is assessed in terms of the CPU time requir

ISSN:0749-159X    

DOI:10.1002/num.1690030402

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

摘要:

AbstractA class of nonlinear implicit one‐step difference methods for quasilinear strongly coupled parabolic systems in cylinderical symmetry is considerd. The main part of the article deals with proving convergence of both the semi‐discrete and the fully discrete approximations. For this purpose, bounds for the inverse difference operators have to be derived previously. This is possible subject to a condition which can be considered as a generalization of the concept “parabolic” to systems. Furthermore, a linearized scheme already used by Düchs some years ago turns out to be nothing but one iteration step of the Newton mehod for solving the complete system of nonlinear difference equations. A surprising improvement on the linearized scheme is achievd, if two or more Newton iterations are p

ISSN:0749-159X    

DOI:10.1002/num.1690030403

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690030404

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690030405

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

摘要:

AbstractWe establish here the convergence (thereby proving the existence) of a semi‐discrete scheme for the quasilinear hyperbolic equationwherex∈Rn,t∈ [0,T], and ϕ ∈L∞(Rn). It is well known that the above problem does not necessarily have global classical solutions and the usual concepts of weak solution. do not lead to a unique solution The existence of a unique solution to the above problem in a suitable sense was established in [3], where a parabolic problem obtained by introducing the term −ϵΔuwas studied and then the behavior as ϵ → 0 was discussed. A difference scheme approach to a problem of the above type where ϕidoes not depend onxandtand Ψ does not depend onuwas also studied in [2]. The aim of this paper is to present a proof for the case when ϕ depends onx, Ψ depends onu, and the technical complications in this case are nontrivial. The discussions in this paper my be considered as continuation of the idea

ISSN:0749-159X    

DOI:10.1002/num.1690030406

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

摘要:

AbstractEngineers have been aware for some time of the phenomenon of superconvergence, whereby there exist (stress) points at which the accuracy of a finite‐element solution is superior to that of the approximation generally. This phenomenon has been treated in recent years by mathematicians who have proved, for certain two‐dimensional second‐order elliptic problems, superconvergent error estimates for retrieved finite‐element derivatives. These results have demanded high global regularity of the solutions of the boundary value problems. In this present article cut‐off functions are used to prove similar superconvergence results over interior subdomains. This allows superconvergence estimates to be derived for problems with solutions of low global regularity, particularly those involving sing

ISSN:0749-159X    

DOI:10.1002/num.1690030407

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

摘要:

AbstractAn interpolation procedure using harmonic splines is described and analyzed for solving (exterior) boundary value problems of Laplace's equation in three dimensions (from discretely given data). The theoretical and computational aspects of the method are discussed. Some numerical examples are given.

ISSN:0749-159X    

DOI:10.1002/num.1690030408

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY

ISSN:0749-159X    

DOI:10.1002/num.1690030401

出版商:John Wiley&Sons, Inc.    

年代:1987

数据来源: WILEY