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Solution for a classical problem in the calculus of variations via rationalized Haar functions. (English) Zbl 1265.49023
Summary: A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is general, and yields accurate results.

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
65K10 Numerical optimization and variational techniques
70Q05 Control of mechanical systems
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