A Modified Ren’s Method with Memory Using a Simple Self-Accelerating Parameter

Abstract

In this paper, a self-accelerating type method is proposed for solving nonlinear equations, which is a modified Ren’s method. A simple way is applied to construct a variable self-accelerating parameter of the new method, which does not increase any computational costs. The highest convergence order of new method is 2 + 6 ≈ 4.4495 . Numerical experiments are made to show the performance of the new method, which supports the theoretical results.

The Existence of Solution of Diffusion Equation with the General Conformable Derivative

“…Most of the above fractional derivatives are defined by their corresponding fractional integrals. Compared with some integral-order partial differential equations such as [9][10][11][12][13][14][15][16][17][18][19], fractional derivatives have hereditary and nonlocal property so that they are much more suitable for describing long-memory processes than the classical integer-order derivatives.…”