A Newton-type technique for solving absolute value equations
Alamgir Khan, Javed Iqbal, Ali Akgül, Rashid Ali, Yuting Du, Arafat Hussain, Kottakkaran Sooppy Nisar, V. Vijayakumar
Abstract
The Newton-type technique is proposed for solving absolute value equations. This new method is a two-step technique with the generalized Newton technique as a predictor and corrector step is the Simpson’s method. Convergence results are established under mild assumptions. The Newton-type technique is very simple and easy to implement. The proposed method is very effective to solve large systems. The heat equation is solved by using the proposed technique. Numerical outcomes show the efficiency of our technique. We add the concluding remarks at the end of this paper.
Topics & Concepts
Newton's methodConvergence (economics)Simple (philosophy)MathematicsType (biology)Applied mathematicsValue (mathematics)Local convergenceMathematical optimizationNonlinear systemIterative methodPhysicsStatisticsEconomicsEcologyEconomic growthBiologyEpistemologyQuantum mechanicsPhilosophyIterative Methods for Nonlinear EquationsMatrix Theory and AlgorithmsAdvanced Optimization Algorithms Research