Abstract General nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem existence uniqueness solution to second-type value given. Finally, for numerical solution, two different approaches illustrated some examples included...

‎in this paper we introduce a numerical approach that solves optimal control problems (ocps)‎‎using collocation methods‎. ‎this approach is based upon b-spline functions‎.‎the derivative matrices between any two families of b-spline functions are utilized to‎‎reduce the solution of ocps to the solution of nonlinear optimization problems‎.‎numerical experiments confirm our theoretical findings‎.