Solution of variational problems by means of a generalized newton-raphson operator

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 two-point 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 Euler-Lagrange 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)

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