Abstract
A boundary integral equation (BIE) formulation is presented for the numerical solution of certain two dimensional nonlinear elliptic equations subject to nonlinear boundary conditions. By applying the Kirchoff transformation, all nonlinear aspects are first transferred to the boundary of the solution domain. Then the accurate solution of problems in which there are boundary singularities is demonstrated by including the analytic nature of the singular solution in only those regions nearest the singularity. Because of this, only a minor modification of the classical nonlinear BIE is required and this results in a substantial improvement in the accuracy of the numerical results throughout the entire solution domain.
The BIE has previously been applied to either nonlinear or singular problems and so the method presently described constitutes an extension in this field.
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© 1984 Springer-Verlag Berlin, Heidelberg
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Ingham, D.B., Kelmanson, M.A. (1984). Solution of Nonlinear Elliptic Equations with Boundary Singularities by an Integral Equation Method. In: Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems. Lecture Notes in Engineering, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82330-5_4
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DOI: https://doi.org/10.1007/978-3-642-82330-5_4
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