We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.
CITATION STYLE
Beshley, A., Chapko, R., & Johansson, B. T. (2019). A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients. In Trends in Mathematics (pp. 493–501). Springer International Publishing. https://doi.org/10.1007/978-3-030-04459-6_47
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