Abstract

This study summary primarily examines the topic of sensitivity analysis in the calculus of variations. In order to determine the boundary value problem, the set of equations, and the partial derivatives (sensitivities) of the objective function value, as well as the primal and dual optimal solutions with consideration to all factors, a perturbation technique is used. The proposed method is demonstrated using two examples of applications, a simple mathematical issue and a slope stability analysis issue which uses a nonstandard problem of the calculus of variations since it is a quotient of integrals. The key contribution of this study is the provision of new theorems (theorem 3.1 and 4.1, see[1]) that allow us to derive simple formulas for the parameters affecting the sensitivities of the target function (finite or infinite). This method enables us to generate closed formulas for the data’s sensitivity to the objective function. The method established in this study is easily applied to more complex calculus of variations scenarios, such as those involving multiple unknown functions, numerous integrals, etc. The sensitivity of BVP and the linear systems of equations and theorems presented in this paper is useful for mathematicians, engineers, and practical researchers in general. This would enable them to include sensitivity analysis in their answers to situations involving calculus of variations, improving the caliber of their work.