Abstract:
This article is dedicated to use of $S$-spline theory for solving equations in partial derivatives. For example, we consider solution of the Poisson equation. $S$-spline — is a piecewise-polynomial function. Its coefficients are defined by two states. The first part of coefficients are defined by smoothness of the spline. The second coefficients are determined by least-squares method. According to order of considered polynomial and number of conditions of first and second type we get $S$-splines with different properties. At this moment we have investigated order 3 $S$-splines of class $C^1$ and order 5 $S$-splines of class $C^2$ (they meet conditions of smoothness of order 1 and 2 respectively). We will consider how the order 3 $S$-splines of class $C^1$ can be applied for solving equation of Poisson on circle and other areas.
\Bibitem{SilKor09}
\by D.~A.~Silaev, D.~O.~Korotaev
\paper Solving of boundary tasks by using $S$-spline
\jour Computer Research and Modeling
\yr 2009
\vol 1
\issue 2
\pages 161--171
\mathnet{http://mi.mathnet.ru/crm633}
\crossref{https://doi.org/10.20537/2076-7633-2009-1-2-161-171}
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https://www.mathnet.ru/eng/crm633
https://www.mathnet.ru/eng/crm/v1/i2/p161
This publication is cited in the following 5 articles:
A. N. Mzedavee, V. I. Rodionov, “Tochnoe reshenie odnoi zadachi optimizatsii, porozhdennoi trekhmernym uravneniem Laplasa”, Izv. IMI UdGU, 51 (2018), 52–78
D. A. Silaev, Zh. G. Ingtem, A. A. Filippov, “Two-sided semi-local smoothing splines”, J. Math. Sci. (N. Y.), 234:4 (2018), 523–530
A. N. Fedosova, D. A. Silaev, “Matematicheskoe modelirovanie izgiba krugovoi plastinki s primeneniem $S$-splainov”, Kompyuternye issledovaniya i modelirovanie, 7:5 (2015), 977–988
A. N. Fedosova, D. A. Silaev, “Mathematical modeling of bending of a circular plate with the use of $S$-splines”, J. Math. Sci., 214:6 (2016), 854–864
D. A. Silaev, “Cubature and quadrature formulas of high order of approximation”, J. Math. Sci., 209:1 (2015), 138–151
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