An efficient direct method for the numerical solution to the Cauchy problem for the Laplace equation. (Russian. English summary) Zbl 07607906
Keywords:
Cauchy problem for Laplace equation; inverse problem; numerical solution; efficient direct methodReferences:
[1] | Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 · Zbl 0499.65030 |
[2] | Lavrent’ev M. M., “O zadache Koshi dlya uravneniya Laplasa”, Izv. AN SSSR. Ser. matem., 20:6 (1956), 819-842 · Zbl 0074.09004 |
[3] | Mukanova B., “Numerical reconstruction of unknown boundary data in the Cauchy problem for Laplace”s equation”, Inverse Problems in Science and Engineering, 21:8 (2012), 1255-1267 · Zbl 1300.65082 · doi:10.1080/17415977.2012.744405 |
[4] | Mukanova B., Maussumbekova S., Kulbay M., “Solving of the regularized inverse problem for elliptic equations in cylindrical coordinates: analytical formulas”, J. of Appl. Mechanics and Materials, 799-800 (2015), 693-697 · Zbl 1433.65263 · doi:10.4028/www.scientific.net/AMM.799-800.693 |
[5] | Kabanikhin S. I., Bektemesov M. A., Ayapbergenova A. T., Nechaev D. V., “Optimization methods of solving continuation problems”, Computational technologies, 9, special iss. (2004), 49-60 |
[6] | Karchevsky A. L., “Reformulation of an inverse problem statement that reduces computational costs”, Eurasian J. of Mathematical and Computer Application, 1:2 (2013), 4-20 |
[7] | Cheng J., Hon Y. C., Wei T., Yamamoto M., “Numerical computation of a Cauchy problem for Laplace”s equation”, ZAMM, 81:10 (2001), 665-674 · Zbl 0999.65100 · doi:10.1002/1521-4001(200110)81:10<665::AID-ZAMM665>3.0.CO;2-V |
[8] | Kabanikhin S. I., Shishlenin M. A., Nurseitov D. B., Nurseitova A. T., Kasenov S. E., “Comparative analysis of methods for regularizing an initial boundary value problem for the Helmholtz equation”, J. of Appl. Math., 2014, special iss. (2014), 1-7 · Zbl 1442.35546 · doi:10.1155/2014/786326 |
[9] | Kabanikhin S. I., Karchevsky A. L., “Method for solving the Cauchy problem for an elliptic equation”, J. of Inverse and Ill-posed Problems, 3:1 (1995), 21-46 · Zbl 0833.65107 · doi:10.1515/jiip.1995.3.1.21 |
[10] | Kabanikhin S. I., Obratnye i nekorrektnye zadachi, Sibirskoe nauchnoe izdatel’stvo, Novosibirsk, 2009 |
[11] | Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravneniy, Nauka, M., 1978 · Zbl 0588.65071 |
[12] | Samarskii A. A., Andreev V. B., Raznostnye metody dlya ellipticheskikh uravneniy, Nauka, M., 1979 |
[13] | Liu C.-S., “An analytical method for the inverse Cauchy problem of Laplace equation in a rectangular plate”, J. of Mechanics, 27:4 (2011), 575-584 · doi:10.1017/jmech.2011.60 |
[14] | Lavrent’ev M. M., “Ob integral”nykh uravneniyakh pervogo roda”, DAN SSSR, 127:1 (1959), 31-33 · Zbl 0107.09904 |
[15] | Lavrent’ev M. M., Savel’ev L. Ya., Teoriya operatorov i nekorrektnye zadachi, 2-e izd., pererab. i dopoln., Izd-vo In-ta matematiki, Novosibirsk, 2010 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.