Abstract
An integral equation method is presented for solving the standard boundary value problem for generalized analytic functions. The method combines a Fredholm equation of the second kind in the domain with Fredholm equations of the first and the second kind on the boundary for single boundary and surface layers. An approximation method for solving these equations is prescribed. The method provides an application for solving semilinear problems by an imbedding method combined with Newton's approximation. For the standard problem a few numerical results are given in the appendix.
Keywords
- Integral Equation
- Singular Integral Equation
- Integral Equation Method
- Homogeneous Boundary Condition
- Riemann Hilbert Problem
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An invited address at the Conference on Constructive and Computational Methods for Differential and Integral Equations, Research Center for Applied Science, Indiana University, Bloomington, February 1974.
This investigation was carried out while the author was a Visiting Unidel Chair Professor at the University of Delaware.
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Wendland, W.L. (1974). An integral equation method for generalized analytic functions. In: Colton, D.L., Gilbert, R.P. (eds) Constructive and Computational Methods for Differential and Integral Equations. Lecture Notes in Mathematics, vol 430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066280
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DOI: https://doi.org/10.1007/BFb0066280
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