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General boundary element method for nonlinear problems. (English) Zbl 0863.76037

Summary: The well-known nonlinear equation \(f'''+{1\over 2}ff''=0\) with boundary conditions \(f(0)=0\), \(f'(0)=0\) and \(f(\infty)=1\) is used as an example to describe the basic ideas of a general boundary element method for nonlinear problems whose governing equations and boundary conditions do not contain any linear terms.

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
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[1] Blasius, Z. Math. Phys. 56 pp 1– (1908)
[2] and , Advances in Boundary Elements 1: Computations and Fundamentals, Computational Mechanics Publications, Southampton, 1989.
[3] Boundary Elements X, Vol. 1, Mathematical and Computational Aspects, Computational Mechanics Publications, Southampton, 1988.
[4] and , Fuehrer Durch die Stroemungslehre, Vieweg, Braunschweig, 1969.
[5] Howarth, Philos. Mag. 42 pp 1433– (1951) · doi:10.1080/14786445108560962
[6] and , ’The generalized BEM for non-linear problems’, in (ed.), Elements X, Vol. 1, Mathematical and Computational Aspects, Computational Mechanics Publications, Southampton, 1988, pp. 1-17.
[7] Liao, Int. j. numer. methods fluids 15 pp 595– (1992)
[8] Liao, Int. j. numer. methods fluids 22 pp 1– (1996)
[9] ’The quite general BEM for strongly non-linear problems’, in , and (eds), Boundary Elements VXII, Computational Mechanics Publications, Southampton, 1995, pp. 67-74. · Zbl 0839.65132
[10] and , The Dual Reciprocity Boundary Element Method, Computational Mechanics Publications/Elsevier, Southampton/Boston, MA, 1992. · Zbl 0758.65071
[11] ’New development in the dual reciprocity method’, in , and (eds), Boundry Elements VXII, Computational Mechanics Publications, Southampton, 1995, pp. 11-18. · Zbl 0839.65123
[12] Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems, Prentice-Hall, Englewood Cliffs, NJ, 1987. · Zbl 0733.65031
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