Abstract
In this work, we have improved the order of the double-step Newton method from four to five using the same number of evaluation of two functions and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each step. The multi-step version converges with order 3r+5, r≥1. Numerical experiments are done comparing the new methods with some existing methods. Our methods are also tested on Chandrasekhar’s problem and the 2-D Bratu problem to illustrate the applications.
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Madhu, K., Babajee, D.K.R. & Jayaraman, J. An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications. Numer Algor 74, 593–607 (2017). https://doi.org/10.1007/s11075-016-0163-2
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DOI: https://doi.org/10.1007/s11075-016-0163-2