Higher even-order convergence and coupled solutions for second-order boundary value problems on time scales

In this paper, for a second-order boundary value problem on time scales, a method of generalized quasilinearization, under coupled upper and lower solutions, is discussed. An attempt for the method is to establish sufficient conditions for generating monotone iterative schemes whose elements converge rapidly to the unique solution of the given problem. Furthermore, the convergence is of order k(k≥2), which is even. Finally, two examples are provided to illustrate our results.