A new stable collocation method for solving a class of nonlinear fractional delay differential equations

In this paper, a stable collocation method for solving the nonlinear fractional delay differential equations is proposed by constructing a new set of multiscale orthonormal bases of$W^{1}_{2,0}$W2,01. Error estimations of approximate solutions are given and the highest convergence order can reach four in the sense of the norm of$W_{2,0}^{1}$W2,01. To overcome the nonlinear condition, we make use of Newton’s method to transform the nonlinear equation into a sequence of linear equations. For the linear equations, a rigorous theory is given for obtaining theirε-approximate solutions by solving a system of equations or searching the minimum value. Stability analysis is also obtained. Some examples are discussed to illustrate the efficiency of the proposed method.