On the solution of differential equation system characterizing curve pair of constant breadth by the Lucas collocation approximation

In this study, for solving linear differential equation system characterizing curve pair of constant breadth according to Bishop frame in Euclidean 3-space, a new collocation method based on Lucas polynomials is introduced and hence the curve pair of constant breadth is determined. Furthermore, an error analysis based on residual error function is given for the method. To demonstrate the accuracy and effciency of the method, an example is given with the help of computer programmes Maple and Matlab