Homotopies and the existence and computation of solutions of systems of nonlinear equations

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Published **1979**
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Written in English

Classifications | |
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LC Classifications | Microfilm 80057 |

The Physical Object | |

Format | Microform |

Pagination | v, 108 l. |

Number of Pages | 108 |

ID Numbers | |

Open Library | OL1368397M |

LC Control Number | 92895694 |

Abstract. This paper describes a globally convergent path-following method for solving nonlinear equations containing particular kinds of nonsmooth functions called normal maps. These normal maps express nonlinear variational inequalities over polyhedral convex sets in a form convenient for analysis and computational by: By numerical examples, it is shown that the proposed algorithm can find all solutions of systems of nonlinear equations in practical computation time. View Show abstract. A procedure is introduced for solving systems of polynomial equations that need to be solved repetitively with varying coefficients. The procedure is based on the cheater’s homotopy, a continuation method that follows paths to all by: The topological degree is indeed a powerful and practically usable tool for proving the existence of robust solutions of systems of the form f = 0 for (nonlinear) continuous functions f: R n.

Computation of all solutions to a system of polynomial equations. Mathematical Programming, Vol. 25, No. 2 Vol. 21, No. 3. Piecewise-Linear Homotopy Algorithms for Sparse Systems of Nonlinear Equations. SIAM Journal on Control and Optimization, Vol. 21, No. 2. Piecewise nonlinear homotopies. 1 December (or solving equations with. Numerical Solution of Systems of Nonlinear Algebraic Equations contains invited lectures of the NSF-CBMS Regional Conference on the Numerical Solution of Nonlinear Algebraic Systems with Applications to Problems in Physics, Engineering and Economics, held on July , In a previous paper, the authors suggested a procedure for obtaining all solutions to certain systems ofn equations inn complex variables. The idea was to start with a trivial system of equations to which all solutions were easily known. The trivial system was then perturbed into the given system. During the perturbation process, one followed the solution paths from each of the trivial. Partial differential equations. ” The problems usually require knowledge of material coming from various chapters. analysis of the solutions of the equations. Operational solution of some partial differential equations. Solution 9. Read this book using Google Play Books app on your PC, android, iOS devices. Open Access Policy.

Contents Preface to the fourth edition vii 1 Second-order differential equations in the phase plane 1 Phase diagram for the pendulum equation 1 Autonomous equations in the phase plane 5 Mechanical analogy for the conservative system x¨=f(x) 14 The damped linear oscillator 21 Nonlinear damping: limit cycles 25 Some applications 32 Parameter-dependent conservative. () Solution Of Bounded Nonlinear Systems Of Equations Using Homotopies With Inexact Restoration. International Journal of Computer Mathematics , () Finding all solutions of piecewise-linear resistive circuits using the dual simplex method. This article deals with the solutions of the existence and uniqueness for a new class of boundary value problems (BVPs) involving nonlinear fractional differential equations (FDEs), inclusions, and boundary conditions involving the generalized fractional integral. The nonlinearity relies on the unknown function and its fractional derivatives in the lower order. Nonlinear OrdinaryDiﬀerentialEquations by Peter J. Olver University of Minnesota 1. Introduction. These notes are concerned with initial value problems for systems of ordinary dif-ferential equations. Here our emphasis will be on nonlinear phenomena and properties, particularly those with physical relevance. Finding a solution to a.

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