The Problem of Bolza in the Calculus of Variations

NON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS

A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence anal...

Sufficient Conditions for the Isoperimetric Problem of Bolza in the Calculus of Variations

Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi Inequalities

We investigate the value function of the Bolza problem of the Calculus of Variations V (t, x) = inf { ∫ t 0 L(y(s), y(s))ds + φ(y(t)) : y ∈W (0, t; IR), y(0) = x }

Sufficient Conditions for the Generalized Problem of Bolza

This paper presents sufficient conditions for strong local optimality in the generalized problem of Bolza. These conditions represent a unification, in the sense that they can be applied to both the calculus of variations and to optimal control problems, as well as problems with nonsmooth data. Also, this paper brings to light a new point of view concerning the Jacobi condition in the classical...

An analytic study on the Euler-Lagrange equation arising in calculus of variations

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...