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  • 1
    Electronic Resource
    Electronic Resource
    A.D.I. Methods for the solution of transient heat conduction problems in r-θ geometry (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1799-1807 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the application of a particular class of computational methods, the alternating direction implicit methods applied to the solution of time dependent heat conduction problems in regions involving circular symmetry is presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620121203
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  • 2
    Electronic Resource
    Electronic Resource
    Boundary value techniques for finite element solutions of the diffusion-convection equation (1986)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 23 (1986), S. 1145-1159 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the formulation of six-point and nine-point finite element equations for the solution of the diffusion-convection equation is presented. The six-point equation requires the solution of a tridiagonal system of equations and the nine-point centred equation is treated as a solution of a boundary value problem which leads to a large linear system of equations.Some numerical experiments are presented and the comparison with existing methods is included.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620230611
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  • 3
    Electronic Resource
    Electronic Resource
    Block overrelaxation methods for non-rectangular co-ordinates (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 49-57 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the application of successive block overrelaxation methods to obtain the deflection of a skew plate are compared, although the techniques herein are applicable to a wider range of problems. An algorithm for the direct solution of the submatrices comprising the two-line blocks of the skew grid is presented and the results are compared with the block (line and peripheral) overrelaxation methods.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190107
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  • 4
    Electronic Resource
    Electronic Resource
    Implementation of an improved bisection algorithm in buckling problems (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1047-1052 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved bisection strategy is presented to determine the eigenvalues of a real symmetric tridiagonal matrix which occurs in a simple column buckling problem. The new strategy, which involves only a minor modification, utilizes incomplete Sturm sequences only as long as relevant information on the next and following eigenvalues is obtained resulting in a minimization of the computational work. The strategy is particularly effective if only a few eigenvalues are required. The technique can be used for a wider class of eigenvalue problems than the illustrative one presented here.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190708
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  • 5
    Electronic Resource
    Electronic Resource
    The D1/2-norm of the SOR and Cyclic Chebyshev Semi-Iterative (CCSI) methods for a class of non-symmetric matrices (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 547-557 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Successive Overrelaxation (SOR) and the Cyclic Chebyshev Semi-Iterative (CCSI) methods are considered for solving the non-symmetric linear systems Ax = b when A has the form \documentclass{article}\pagestyle{empty}\begin{document}$$ {\bf A} = \left({\begin{array}{*{20}c} {{\bf D}_1} & {\bf F} \\ {-{\bf F}^{\rm T}} & {{\bf D}_{\rm 2}}\\ \end{array}} \right) $$\end{document} with D1 and D2 symmetric positive definite (SPD).The D1/2-norms of both methods are determined and it is shown that, though the SOR method is better based on the spectral radius, the CCSI scheme is far better than SOR according to the D1/2-norm.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270308
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  • 6
    Electronic Resource
    Electronic Resource
    Use of modified bisection algorithm for the vibrating beam problem (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 1 (1985), S. 17-22 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, the implementation of the incomplete Sturm sequence evaluation of Evans et al. 2 is considered for the determination of the eigenvalues of a symmetric quindiagonal matrix A which occurs in vibrating beam problems. The method based on triangularization by elementary stabilized matrices involving the application of the bisection method for quindiagonal matrices is fully described in Sentance and Cliff, 3 and therefore only the changes to the proposed method in order to obtain high efficiency when dealing with several of the lowest or highest eigenvalues of quindiagonal matrices are discussed. The paper concludes with the FORTRAN program and the supporting numerical evidence.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630010105
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  • 7
    Electronic Resource
    Electronic Resource
    High order difference group explicit (HODGE) methods (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 449-462 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Point iterative methods at which, at any one time, only a single equation of the linear system is treated are well known. However, in recent times block (or line) iterative methods, in which a group of equations (or points on the grid mesh) are treated implicity and solved directly by a specialized algorithm, have become the standard techniques for solving the sparse linear systems derived from the finite difference/element discretization of a self-adjoint elliptic partial differential equation on a two-dimensional grid. The main concern of this paper is to construct new groupings of the mesh points of the network into four and nine points using the high order accurate nine-point finite difference equations and to investigate their advantages when used explicity in the standard iterative methods4,5,6.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020502
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