A hybrid analysis direct method in the calculus of variations

被引：30

作者：

Razzaghi, M ^{[1
]}

Marzban, HR

机构：

[1] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

[2] Amirkabir Univ, Dept Math, Tehran, Iran

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2000年 / 75卷 / 03期

关键词：

calculus of variations; direct method; hybrid functions; Legendre polynomials; block-pulse functions;

D O I：

10.1080/00207160008804982

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a direct method for finding the solution of variational problems using a hybrid function. The properties of hybrid functions which consists of block-pulse functions plus Legendre polynomials are presented. An operational matrix of integration and the cross product of two hybrid function vectors are used to reduce a variational problem to the solution of algebraic equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.

引用

页码：259 / 269

页数：11

共 9 条

[1] SHIFTED LEGENDRE DIRECT METHOD FOR VARIATIONAL-PROBLEMS [J].

CHANG, RY ;

WANG, ML .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1983, 39 (02) :299-307

[2] WALSH SERIES DIRECT METHOD FOR SOLVING VARIATIONAL PROBLEMS [J].

CHEN, CF ;

HSIAO, CH .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1975, 300 (04) :265-280

[3]

Elsgolic L. E., 1962, CALCULUS VARIATIONS

[4] SHIFTED TSCHEBYSCHEFF DIRECT METHOD FOR SOLVING VARIATIONAL-PROBLEMS [J].

HORNG, IR ;

CHOU, JH .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1985, 16 (07) :855-861

[5] LAGUERRE SERIES DIRECT METHOD FOR VARIATIONAL-PROBLEMS [J].

HWANG, C ;

SHIH, YP .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1983, 39 (01) :143-149

[6] THE OPERATIONAL MATRIX OF INTEGRATION FOR BESSEL-FUNCTIONS [J].

PARASKEVOPOULOS, PN ;

SKLAVOUNOS, PG ;

GEORGIOU, GC .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1990, 327 (02) :329-341

[7] FOURIER-SERIES DIRECT METHOD FOR VARIATIONAL-PROBLEMS [J].

RAZZAGHI, M ;

RAZZAGHI, M .

INTERNATIONAL JOURNAL OF CONTROL, 1988, 48 (03) :887-895

[8]

RAZZAGHI M, 1989, J FRANKLIN I, V326, P215

[9]

SCHECHTER RS, 1967, VARIATION METHOD ENG

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