Globally convergent homotopy methods: a tutorial
TLDR
Homotopy algorithms for solving nonlinear systems of (algebraic) equations, which are convergent for almost all choices of starting point, are globally convergent with probability one and exhibit a large amount of coarse grain parallelism.About:
This article is published in Applied Mathematics and Computation.The article was published on 1989-05-01 and is currently open access. It has received 123 citations till now. The article focuses on the topics: n-connected & Homotopy analysis method.read more
Citations
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Book
Introduction to Numerical Continuation Methods
Eugene L. Allgower,Kurt Georg +1 more
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
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Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms
TL;DR: Changes to HOMPACK include numerous minor improvements, simpler and more elegant interfaces, use of modules, new end games, support for several sparse matrix data structures, and new iterative algorithms for large sparse Jacobian matrices.
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The homotopy analysis method to solve the Burgers–Huxley equation
A. Molabahrami,Farzad Khani +1 more
TL;DR: In this paper, an analytical technique, namely the homotopy analysis method (HAM), is applied to obtain an approximate analytical solution of the Burgers-Huxley equation.
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Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient
TL;DR: In this article, the authors used the homotopy analysis method (HAM) to evaluate the analytical approximate solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient.
References
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The solution of nonlinear operator equations by a-stable integration techniques
TL;DR: It is well known that a damped or underrelaxed Newton method will sometimes solve a system of nonlinear equations when the full Newton method cannot as discussed by the authors. This happens, for example, when only a poor...
HOMPACK: a suite of codes for globally convergent homotopy algorithms. Technical report No. 85-34
TL;DR: HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation based, normal flow, and augmented Jacobian matrix.
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Computational Methods of Linear Algebra.
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Initial Value Methods for Boundary Value Problems@@@Invariant Imbedding and its Applications to Ordinary Differential Equations. An Introduction
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An Algorithm That is Globally Convergent with Probability One for a Class of Nonlinear Two-Point Boundary Value Problems
TL;DR: In this paper, the Chow-Yorke algorithm was applied to a class of nonlinear two-point boundary value problems by solving the nonlinear system of equations defined by shooting.