B-Spline Solutions of General Euler-Lagrange Equations
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....
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
MDPI AG
2019-04-01
|
Series: | Mathematics |
Subjects: | |
Online Access: | https://www.mdpi.com/2227-7390/7/4/365 |
id |
doaj-977098d9c94f40ecab2719a86b0f9d86 |
---|---|
record_format |
Article |
spelling |
doaj-977098d9c94f40ecab2719a86b0f9d862020-11-24T20:42:09ZengMDPI AGMathematics2227-73902019-04-017436510.3390/math7040365math7040365B-Spline Solutions of General Euler-Lagrange EquationsLanyin Sun0Chungang Zhu1School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, ChinaSchool of Mathematical Sciences, Dalian University of Technology, Dalian 116023, ChinaThe 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.https://www.mdpi.com/2227-7390/7/4/365Lagrangian functionalEuler-Lagrange equationB-spline surfacesharmonic operator |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lanyin Sun Chungang Zhu |
spellingShingle |
Lanyin Sun Chungang Zhu B-Spline Solutions of General Euler-Lagrange Equations Mathematics Lagrangian functional Euler-Lagrange equation B-spline surfaces harmonic operator |
author_facet |
Lanyin Sun Chungang Zhu |
author_sort |
Lanyin Sun |
title |
B-Spline Solutions of General Euler-Lagrange Equations |
title_short |
B-Spline Solutions of General Euler-Lagrange Equations |
title_full |
B-Spline Solutions of General Euler-Lagrange Equations |
title_fullStr |
B-Spline Solutions of General Euler-Lagrange Equations |
title_full_unstemmed |
B-Spline Solutions of General Euler-Lagrange Equations |
title_sort |
b-spline solutions of general euler-lagrange equations |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2019-04-01 |
description |
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. |
topic |
Lagrangian functional Euler-Lagrange equation B-spline surfaces harmonic operator |
url |
https://www.mdpi.com/2227-7390/7/4/365 |
work_keys_str_mv |
AT lanyinsun bsplinesolutionsofgeneraleulerlagrangeequations AT chungangzhu bsplinesolutionsofgeneraleulerlagrangeequations |
_version_ |
1716823097541132288 |