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  • 1
    Electronic Resource
    Electronic Resource
    A Simple Approach of Enlarging Convergence Regions of Perturbation Approximations (1999)
    Springer
    Nonlinear dynamics 19 (1999), S. 93-111 
    Details
    ISSN: 1573-269X
    Keywords: homotopy analysis method ; enlarging convergence region ; general Taylor theorem ; Van der Pol equation ; Riccati equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a simple approach to enlarging convergence regions of perturbation approximations is proposed. Based on the so-called general Taylor theorems, this approach has a solid mathematical foundation. Moreover, it is rather simple to apply. Two nonlinear equations, the Riccati equation and the Van der Pol equation are used as examples to illustrate the validity and the great potential of this approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008373627897
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS. PART 2: SOME 2D EXAMPLES (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 863-873 
    Details
    ISSN: 0271-2091
    Keywords: general BEM ; general non-linear differential operator ; homotopy ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the general BEM proposed previously by Liao is applied to solve some 2D strongly non-linear differential equations, even including those whose governing equations and boundary conditions do not contain any linear terms. It is shown that the proposed general BEM is really valid for general non-linear problems, so that it can be applied to solve high-dimensional, strongly non-linear problems in engineering. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 863-873, 1997.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    HIGH-ORDER BEM FORMULATIONS FOR STRONGLY NON-LINEAR PROBLEMS GOVERNED BY QUITE GENERAL NON-LINEAR DIFFERENTIAL OPERATORS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 739-751 
    Details
    ISSN: 0271-2091
    Keywords: general BEM ; general non-linear differential operator ; homotopy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the basic idea of homotopy in topology is applied to give a kind of high-order BEM formulation for general non-linear problems governed by non-linear differential operators which need not contain any linear operators at all. As a result, the traditional BEM for non- linear problems is just a special case of the proposed method. Three simple examples are used to show the effectiveness of the proposed quite general BEM for non-linear problems.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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