Narrow Results

This paper presents a new numerical iteration method for solving the absolute value equations. The proposed method uses the generalized Newton method as a predictor step, and the five-point open Newton–Cotes formula is considered the corrector step. The convergence of the proposed method is studied in detail. The proposed method solves large systems effectively due to its simplicity and effectiveness. In this paper, we have solved the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solved it using the proposed method. Several numerical examples were provided to demonstrate the accuracy and effectiveness of the new approach. In addition, the novel approach solves absolute value equations with greater accuracy and precision than other existing methods.

This paper describes two new iterative algorithms for determining absolute value equations. The algorithms are based on a splitting of the coefficient matrix. Moreover, we analyze the convergence effects of the presented algorithms via some theorems. Eventually, numerical tests are provided to confirm the credibility of our procedures.