Modified Jacobian Newton Iterative Method : Theory and Applications

Abstract EN

This article proposes a new approach to the construction of a linearization method based on the iterative operator-splitting method for nonlinear differential equations.

The convergence properties of such a method are studied.

The main features of the proposed idea are the linearization of nonlinear equations and the application of iterative splitting methods.

We present an iterative operator-splitting method with embedded Newton methods to solve nonlinearity.

We confirm with numerical applications the effectiveness of the proposed iterative operator-splitting method in comparison with the classical Newton methods.

We provide improved results and convergence rates.