Generation of root finding algorithms via perturbation theory and some formulas
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Publication:879553
DOI10.1016/j.amc.2006.05.207zbMath1115.65056OpenAlexW2019374578WikidataQ58206701 ScholiaQ58206701MaRDI QIDQ879553
Hakan Boyaci, Mehmet Pakdemirli
Publication date: 14 May 2007
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.207
perturbation theorynumerical examplesNewton-Raphson methodAdomian decomposition methodroot finding algorithmshigher order iteration formulasHouseholder's iteration
Related Items (16)
Estimating roots of polynomials using perturbation theory ⋮ New perturbation iteration solutions for Fredholm and Volterra integral equations ⋮ Numerical solution of pantograph-type delay differential equations using perturbation-iteration algorithms ⋮ Perturbation-iteration method for first-order differential equations and systems ⋮ A class of iterative methods with third-order convergence to solve nonlinear equations ⋮ Simple geometry facilitates iterative solution of a nonlinear equation via a special transformation to accelerate convergence to third order ⋮ Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method ⋮ Effective root-finding methods for nonlinear equations based on multiplicative calculi ⋮ A simple algorithm for high order Newton iteration formulae and some new variants ⋮ Two-parameter homotopy method for nonlinear equations ⋮ A comprehensive perturbation theorem for estimating magnitudes of roots of polynomials ⋮ Perturbation theorems for estimating magnitudes of roots of polynomials ⋮ New perturbation-iteration solutions for Bratu-type equations ⋮ Newton's method's basins of attraction revisited ⋮ Approximate solution of time-fractional fuzzy partial differential equations ⋮ A note on the convergence of the irrational Halley’s iterative algorithm for solving nonlinear equations
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