In this article we consider iterative operator-splitting methods for nonlinear differential equations. The main feature of the proposed idea is the embedding of Newton’s method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed...

In this article we consider iterative operator-splitting methods for nonlinear differential equations with respect to their eigenvalues. The main feature of the proposed idea is the fixed-point iterative scheme that linearizes our underlying equations. Based on the approximated eigenvalues of such linearized systems we choose the order of the the operators for our iterative splitting scheme. Th...

A new type ð2; 2Þ-step iterative method related to an optimal Chebyshev method is developed for solving real and nonsymmetric linear systems of the form Ax 1⁄4 b. It is an extension of the ð2; 2Þ-step iterative method introduced in [Numer. Linear Algebra Appl. 7 (2000) 169]. The superiority of the new type ð2; 2Þ-step iterative method over the optimal Chebyshev method is derived in the case whe...