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Spline-interpolation solution of Cauchy problem for a harmonic function in a simply connected 3D domain | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 1، خرداد 2026، صفحه 315-325 اصل مقاله (3.3 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.29691.2646 | ||
| نویسندگان | ||
| Elena Shirokova1؛ Pyotr Ivanshin* 2 | ||
| 1Lobachevskiy Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya st., 35, Kazan, 420008, Russia | ||
| 2Kazan National Research Technical University, K. Marksa st., 10, Kazan, 420111, Russia | ||
| چکیده | ||
| Here we construct an approximate spline-interpolation solution of the Cauchy problem for the Laplace equation. Our construction describes two different methods based on solution of integral equations. The first method involves singular integral equation, and the second one is based on solution of a Fredholm equation. We present the linear and the polynomial examples clarifying the construction approaches. | ||
| کلیدواژه‌ها | ||
| Cauchy problem؛ integral equation؛ holomorphic function؛ spline؛ approximate solution | ||
| مراجع | ||
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[1] R.A. Blaya, J.B. Reyes, F. Brackx, H.D. Schepper, F. Sommen, Cauchy integral formulae in quaternionic hermitean Clifford analysis, Complex Anal. Oper. Theory 6 (2012) 971-985. [2] R.A. Blaya, M.A. Alfaro, Complex and quaternionic Cauchy formulas in Koch snowflakes, Complex Var. Elliptic Equ. 67 (2022) 1287–1298. [3] J.J.C. Mones, L.H.O. Valencia, J.J.O. Oliveros, D.A. Velasco, Stable numerical solution of the Cauchy problem for the Laplace equation in irregular annular regions, Numer. Methods Partial Differ. Equ. 33 (2017) 1799-1822. [4] F.D. Gakhov, Boundary Value Problems, Dover Publications, 1990. [5] P.N. Ivanshin, E.A. Shirokova, Spline-interpolation solution of 3D Dirichlet problem for a certain class of solids, IMA J. Appl. Math. 78 (2013) 1109-1129. [6] E.A. Shirokova, P.N. Ivanshin, On Cauchy problem solution for a harmonic function in a simply connected domain, Issues of Analysis, 12 (2023) 87-96. [7] P.N. Ivanshin, E.A. Shirokova, On Cauchy Problem Solution for a Harmonic Function in a Simply Connected Domain with Multi-Component Boundary, Int. J. Comput. Methods 22 (2025) 2450043. [8] P.N. Ivanshin, E.A. Shirokova, The Approximate Conformal Mapping of a Disk onto Domain with an Acute Angle, Int. J. Appl. Comput. Math. 9 (2023) 54. [9] M.M. Lavrentev, V.G. Romanov, S.P. Shishatskiy, Ill-posed Problems of Mathematical Physics and Analysis, American Mathematical Society, 1986. [10] N.I. Muskhelishvili, Singular Integral Equations, Dover Publications, 2011. [11] G.T. Symm, An integral equation method in conformal mapping, Numer. Math. 9 (1966) 250–258. [12] N. Tarkhanov, The Cauchy Problem for Solutions of Elliptic Equations, Akademie-Verlag, Berlin, 1995. | ||
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