Hybrid Fourier and block-pulse functions for applications in the calculus of variations

If we divide the interval [0, 1] into N sub-intervals, then hybrid Fourier and block-pulse functions on each sub-interval can approximate any function. This ability helps us to have more accurate approximations of piecewise continuous functions. Hence we obtain more accurate solutions to problems in the calculus of variations. In this article, we use a combination of Fourier and block-pulse functions on the interval [0, 1] to solve a variational problem in the solution of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the technique.