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  • 1
    Electronic Resource
    Electronic Resource
    Nutrition of Bacteria and Fungi (1951)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Microbiology 5 (1951), S. 121-138 
    Details
    ISSN: 0066-4227
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Biology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.mi.05.100151.001005
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Numerically solving non-linear problems by the homotopy analysis method (1997)
    Springer
    Computational mechanics 20 (1997), S. 530-540 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, the Homotopy Analysis Method (HAM) proposed by Liao (1992a, 1992b, 1992c, 1992e, 1995a, 1997a) is greatly improved by introducing a nonzero variable ℏ. Based on the HAM, a new numerical approach for strongly non-linear problems is proposed and applied to solve, as an example, a non-linear heat transfer problem, i.e. microwave heating of an unit plate, so as to verify its validity and great potential. Our numerical experiments show that, by the proposed approach, iteration is not absolutely necessary for solving non-linear problems. This fact may deepen our understanding about numerical techniques for non-linear problems and widen our field of vision. Moreover, the basic ideas proposed in this paper may afford us a great possibility to greatly improve our current numerical techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050273
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Higher-order streamfunction-vorticity formulation of 2D steady-state Navier-Stokes equations (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 595-612 
    Details
    ISSN: 0271-2091
    Keywords: 2D Navier-Stokes equation ; Streamfunction-Vorticity formulation ; Regular boundary element method ; Linearity invariance under 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: Based on regular boundary element method and a kind of linearity invariance under homotopy, a kind of numerical scheme of 2D steady-state Navier-Stokes equation in streamfunction-vorticity formulation is described. The flow inside a square cavity is used to illustrate this numerical scheme.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150507
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A general numerical method for solution of gravity wave problems. Part 2: Steady nonlinear gravity waves (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 14 (1992), S. 1173-1191 
    Details
    ISSN: 0271-2091
    Keywords: Steady non-linear water waves ; Potential flow ; Continuous mapping ; 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: A type of numerical scheme for 2D and 3D steady non-linear water wave problems is described. It is based on the finite process method and is insensitive to initial solutions. The relationship between the finite process method and iterative techniques is discussed. As a numerical example the flow past a submerged vortex is solved and the results are compared with those of other authors.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650141004
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    A general numerical method for the solution of gravity wave problems. Part 1: 2D steep gravity waves in shallow water (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 12 (1991), S. 727-745 
    Details
    ISSN: 0271-2091
    Keywords: Non-linear gravity waves ; Velocity potential ; Transformation from non-linear to linear ; 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, 2D steep gravity waves in shallow water are used to introduce and examine a new kind of numerical method for the solution of non-linear problems called the finite process method (FPM). On the basis of the velocity potential function and the FPM, a numerical method for 2D non-linear gravity waves in shallow water is described which can be applied to solve 3D problems, e.g. the wave resistance of a ship moving in deep or shallow water. The convergence is examined and a comparison with the results of other authors is made.The FPM can successfully avoid the use of iterative methods and therefore can overcome the disadvantages and limitations of such methods. In contrast to iterative methods, the FPM is insensitive to the selection of the initial solution and the number of unknowns. The basic idea of the FPM can be used to solve other non-linear problems. Its disadvantage is that much more CPU time is needed to obtain a sufficiently accurate result.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650120804
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    GENERAL BOUNDARY ELEMENT METHOD FOR NON-LINEAR PROBLEMS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 467-483 
    Details
    ISSN: 0271-2091
    Keywords: general BEM ; non-linear operators ; 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 well-known non-linear equation f‴+½ff″=0 with boundary conditions f(0)=0, f′(0)=0 and f (∞)=1 is used as an example to describe the basic ideas of a kind of general boundary element method for non-linear problems whose governing equations and boundary conditions may not contain any linear terms at all.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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