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The computation of water waves modelled by Nekrasov’s equation. (English) Zbl 0780.76059

Nekrasov’s integral equation, describing water waves of almost extreme form, is solved numerically. The method consists of applying a simple quadrature rule to a rearranged version of the original equation. Strongly graded meshes are used to resolve an expected boundary layer in the solution. For methods based on the trapezoidal rule, global bifurcation theory is used to prove, for fixed discretization parameter \(n\), the existence of a continuous branch of positive numerical solutions.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
65R20 Numerical methods for integral equations
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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