## The Numerical solution of nonlinear problems |

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### Contents

Introduction to nonlinear algebraic equations | 3 |

APPROXIMATION | 4 |

Methods for systems of algebraic equations | 20 |

Copyright | |

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### Common terms and phrases

A-stable algebraic algorithm Allgower and Georg applied approach approximation assume Banach space bifurcation point Bohl boundary conditions boundary value problems bounded Broyden calculate Chapter coefficients computed consider convex corresponding curve defined described discrete discussed eigenvalue error example exists Figure finite difference fixed point formulae Frechet derivative function Galerkin method given gives global hence implementation implies initial value problem integral equations inverse isolated solution Jacobian matrix Keller limit points linear maximum norm Newton iteration Newton's method nonlinear equations norm obtain operator ordinary differential equations Ortega parameter partial differential equations perturbation polynomial processors properties quadratic quadrature quasi-Newton quasi-Newton method rate of convergence result RK methods satisfies scalar scheme sequence shown simplex simplices singular smooth solution branch solving stability step stepsize stiff problems strong uniqueness sufficiently suitable techniques theorem trivial solution update variable vector zeros