An Ostrowski-type method with memory using a novel self-accelerating parameter

In this paper, an Ostrowski-type method with memory is proposed for solving nonlinear equations. To this end, we first present an optimal fourth-order Ostrowski-type method without memory. Based on this method without memory, an Ostrowski-type method with memory is given by using a simple self-accelerating parameter. The new self-accelerating parameter is constructed by a novel way and has the properties of simple structure and easy calculation, which do not increase the computational cost of the iterative method. The convergence order of the new iterative method is increased from 4 to 2+5≈4.2361, (5+13)/2≈4.30278 and 2+6≈4.4495, respectively. Numerical experiments are made to show the performance of the new method, which support the theoretical results. From the comparison with some known methods, it is observed that the new method occupies less computing time.