THE NEWTON–RAPHSON METHOD AND ADAPTIVE ODE SOLVERS
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The Newton–Raphson method for solving nonlinear equations f(x) = 0 in ℝn is discussed within the context of ordinary differential equations. This framework makes it possible to reformulate the scheme by means of an adaptive step size control procedure that aims at reducing the chaotic behavior of the original method without losing the quadratic convergence close to the roots. The performance of the modified scheme is illustrated with a few low-dimensional examples.
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2019 ◽
Vol 350
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pp. 396-411
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2008 ◽
Vol 403
(2-3)
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pp. 464-468
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2016 ◽
Vol 33
(3)
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pp. 607-620
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