Next Article in Journal
Reformulated Zagreb Indices of Some Derived Graphs
Previous Article in Journal
Certain Chebyshev-Type Inequalities Involving Fractional Conformable Integral Operators
Previous Article in Special Issue
NLP Formulation for Polygon Optimization Problems
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle

B-Spline Solutions of General Euler-Lagrange Equations

1
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China
2
School of Mathematical Sciences, Dalian University of Technology, Dalian 116023, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 365; https://doi.org/10.3390/math7040365
Received: 28 March 2019 / Revised: 13 April 2019 / Accepted: 15 April 2019 / Published: 22 April 2019
(This article belongs to the Special Issue Discrete and Computational Geometry)
  |  
PDF [847 KB, uploaded 22 April 2019]
  |  

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. View Full-Text
Keywords: Lagrangian functional; Euler-Lagrange equation; B-spline surfaces; harmonic operator Lagrangian functional; Euler-Lagrange equation; B-spline surfaces; harmonic operator
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Sun, L.; Zhu, C. B-Spline Solutions of General Euler-Lagrange Equations. Mathematics 2019, 7, 365.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top