An Efficient Direct Method for Numerically Solving the Cauchy Problem for Laplace’s Equation

Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Solutions of Ill-Posed Problems),Moscow: Nauka, 1979.

Lavrentiev, M.M., On the Cauchy Problem for Laplace’s Equation, Izv. Akad. Nauk SSSR, 1956, vol. 20, no. 6, pp. 819–842.

Mukanova, B., Numerical Reconstruction of Unknown Boundary Data in the Cauchy Problem for Laplace’s Equation, Inv. Probl. Sci. Engin., 2012, vol. 21, iss. 8, pp. 1255–1267.

Mukanova, B., Maussumbekova, S., and Kulbay, M., Solving the Regularized Inverse Problem for Elliptic Equations in Cylindrical Coordinates: Analytical Formulas, J. Appl. Mech. Mater., 2015, vols. 799/800, pp. 693–697.

Kabanikhin, S.I., Bektemesov, M.A., Ayapbergenova, A.T., and Nechaev, D.V., Optimization Methods of Solving Continuation Problems, Comput. Technol., 2004, vol. 9, special iss, pp. 49–60.

Karchevsky, A.L., Reformulation of an Inverse Problem Statement That Reduces Computational Costs, Euras. J. Math. Comp. Appl., 2013, vol. 1, iss. 2, pp. 4–20.

Cheng, J., Hon, Y.C., Wei, T., and Yamamoto, M.,NumericalComputation of a Cauchy Problem for Laplace’s Equation, ZAMM, 2001, vol. 81, iss. 10, pp. 665–674.

Kabanikhin, S.I., Shishlenin, M.A., Nurseitov, D.B., Nurseitova, A.T., and Kasenov, S.E., Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation, J. Appl. Math., 2014, vol. 2014, special iss, pp. 1–7.

Kabanikhin, S.I. and Karchevsky, A.L., Method for Solving the Cauchy Problem for an Elliptic Equation, J. Inv. Ill-Posed Problems, 1995, vol. 3, iss. 1, pp. 21–46.

Kabanikhin, S.I., Obratnye i nekorrektnye zadachi (Inverse and Ill-Posed Problems), Novosibirsk: Sibirskoe Nauch. Izd., 2009.

Samarskii, A.A. and Nikolayev, E.S., Metody resheniya setochnykh uravnenii (Methods of Solving Grid Equations), Moscow: Nauka, 1978.

Samarskii, A.A. and Andreyev, V.B., Raznostnye metody dlya ellipticheskikh uravnenii (Difference Methods for Elliptic Equations), Moscow: Nauka, 1979.

Liu, C.-S., An Analytical Method for the Inverse Cauchy Problem of Laplace Equation in a Rectangular Plate, J.Mech., 2011, vol. 27, iss. 4, pp. 575–584.

Lavrentiev, M.M., On Integral Equations of the First Kind, Dokl. Akad. Nauk SSSR, 1959, vol. 127, no. 1, pp. 31–33.

Lavrentiev, M.M. and Saveliev, L.Ya., Teoriya operatorov i nekorrektnye zadachi (Operator Theory and Ill-Posed Problems), Novosibirsk: Publ. House of the Institute ofMathematics, 2010.