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Solving of boundary tasks by using S-spline

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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 C1 and order 5 S-splines of class C2 (they meet conditions of smoothness of order 1 and 2 respectively). We will consider how the order 3 S-splines of class C1 can be applied for solving equation of Poisson on circle and other areas.

Keywords: S-spline theory, Poisson equation, differential equations solving
Citation in English: Silaev D.A., Korotaev D.O. Solving of boundary tasks by using S-spline // Computer Research and Modeling, 2009, vol. 1, no. 2, pp. 161-171
Citation in English: Silaev D.A., Korotaev D.O. Solving of boundary tasks by using S-spline // Computer Research and Modeling, 2009, vol. 1, no. 2, pp. 161-171
DOI: 10.20537/2076-7633-2009-1-2-161-171
• , . Mathematical modeling of bending of a circular plate using $S$-splines. // Computer Research and Modeling. 2015. — V. 7, no. 5. — P. 977.
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