C~k Spline Functions; a New Discretization Method for Generalized Lagrangian Systems

摘要

Several approaches for discretizing a system of partial differential equations (PDEs) into ordinary differential equations (ODEs) have been elaborated over the last few years. Examples include the collocation method, the nodal space representation, etc. Many of these approaches leads to inefficient models for the control of complex or nonlinear systems. C~k spline function i.e. function which generates k times continuous and derivable approximations, seem to be efficient in several applied non-linear differential problems, optimal control, simulation, or discretization method. This paper proposes a method based on C~k spline functions which gives a C~k spline approximation of the solution and leads to ODEs with k arbitraly fixed.