B-Spline Solutions of General Euler-Lagrange Equations

Lanyin Sun and Chungang Zhu
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Lanyin Sun: School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
Chungang Zhu: School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China

Mathematics, 2019, vol. 7, issue 4, 1-12

Abstract: The Euler-Lagrange equations are useful for solving optimization problems in mechanics. In this paper, we study the B-spline solutions of the Euler-Lagrange equations associated with the general functionals. The existing conditions of B-spline solutions to general Euler-Lagrange equations are given. As part of this work, we present a general method for generating B-spline solutions of the second- and fourth-order Euler-Lagrange equations. Furthermore, we show that some existing techniques for surface design, such as Coons patches, are exactly the special cases of the generalized Partial differential equations (PDE) surfaces with appropriate choices of the constants.

Keywords: Lagrangian functional; Euler-Lagrange equation; B-spline surfaces; harmonic operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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