Conference publications

Solving of boundary tasks by using S-spline

Silaev D. A., Korotaev D. O.

Russia, Moscow

"Математика. Компьютер. Образование". Cб. трудов XIII международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2006. Vol. 2, 498pp. Pp. 85-104.

This article is dedicated to use of S-spline theory for solving equations in partial derivatives. For example, we consider solving of Puasson equation. S-spline – is a piecewise-polynomial. Its coefficients are defined by two states. Its first part of coefficients are defined by smoothness of spline. The least 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 C1 and order 5 S-splines of class C2 (they meets conditions of smoothness of order 1 and 2 accordinally). We will consider how the order 3 S-splines of class C1 can be applied for solving equation of Puasson on circle and on other areas.

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