
Accession Number : AD0481845
Title : SOLUTION OF VARIATIONAL PROBLEMS BY MEANS OF A GENERALIZED NEWTONRAPHSON OPERATOR.
Descriptive Note : Research rept.,
Corporate Author : GRUMMAN AIRCRAFT ENGINEERING CORP BETHPAGE NY RESEARCH DEPT
Personal Author(s) : McGill, Robert ; Kenneth, Paul
Report Date : MAY 1964
Pagination or Media Count : 28
Abstract : This paper presents the development of an indirect method for solving variational problems by means of an algorithm for obtaining the solution to the associated nonlinear twopoint boundary value problem. The method departs from the usual indirect procedure of successively integrating the nonlinear equations and adjusting arbitrary initial conditions until the remaining boundary conditions are satisfied. Instead, an operator is introduced which produces a sequence of sets of functions which satisfy the boundary conditions but in general do not satisfy the nonlinear system formed by the state equations and the EulerLagrange equations. Under appropriate conditions this sequence converges uniformly and rapidly (quadratically) to the solution of the nonlinear boundary value problem. The computational effectiveness of the algorithm is demonstrated by three numerical examples. (Author)
Descriptors : (*BOUNDARY VALUE PROBLEMS, OPERATORS(MATHEMATICS)), NONLINEAR DIFFERENTIAL EQUATIONS, ALGORITHMS, NUMERICAL METHODS AND PROCEDURES, SET THEORY, NUMERICAL INTEGRATION, SEQUENCES(MATHEMATICS), NUMERICAL ANALYSIS, OPTIMIZATION, DIGITAL COMPUTERS, DIFFERENTIAL EQUATIONS, EQUATIONS, COMPUTER PROGRAMMING, MATHEMATICAL MODELS, NONLINEAR SYSTEMS, CALCULUS OF VARIATIONS.
Subject Categories : Theoretical Mathematics
Computer Programming and Software
Computer Hardware
Distribution Statement : APPROVED FOR PUBLIC RELEASE