Semi-local convergence of a sixth-order iterative method for solving nonlinear systems

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Abstract

This paper verifies the semi-local convergence of a sixth-order iterative method for solving nonlinear systems. In the proof, the recursive relation method is used to prove the semi- local convergence of the iterative method in Banach spaces. The proof process outlined above does not necessitate the higher-order continuous differentiability of the functionL(u). The advantage of the iterative method is that by employing auxiliary sequences and functions, convergence can be established using only first-order Fréchet derivatives. The proposed sixth-order method reduces computational costs compared to existing sixth-order methods by requiring only one LU decomposition per iteration instead of two. Finally, this sixth-order iterative approach is utilized for solving Hammerstein equations along with real gas equation of state. The experimental results prove the effectiveness of the iterative method.

Keywords

nonlinear equations / semi-local convergence / recurrence relation / domain of existence and uniqueness

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