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Shooting-Projection Method for Two-Point Boundary Value Problems
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TLDR
A novel shooting method for solving two-point boundary value problems for second order ordinary differential equations using an auxiliary function that satisfies both boundary conditions and minimizes the H1 semi-norm of the difference between itself and the initial value problem solution.Abstract:
This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula to correct the initial condition; the process is repeated until the second boundary condition is satisfied. The iteration formula is derived utilizing an auxiliary function that satisfies both boundary conditions and minimizes the H1 semi-norm of the difference between itself and the initial value problem solution.read more
Citations
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O.K. Koriko,Isaac Lare Animasaun,Basavarajappa Mahanthesh,Salman Saleem,G. Sarojamma,R. Sivaraj +5 more
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Alternating Minimization Algorithm for Polynomial Optimal Control Problems
Changhuang Wan,Ran Dai,Ping Lu +2 more
TL;DR: Many optimal control problems can be cast into polynomial optimization problems through the discretization and conversion of expressions.
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Solution of two point boundary value problems, a numerical approach: parametric difference method
TL;DR: In this article, a parametric finite difference method was proposed for the solution of two point boundary value problems in ordinary differential equations with mixed boundary conditions, and the results obtained for the model problem with constructed exact solution depends on the choice of parameters.
Journal ArticleDOI
Replacing the finite difference methods for nonlinear two-point boundary value problems by successive application of the linear shooting method
TL;DR: It is proved that using finite differences to discretize the sequence of linear differential equations arising from quasi-linearization leads to the usual iteration formula of the Newton finite difference method, and a way of replacing the Newton, Picard, and constant-slope finite difference methods by respective successive application of the linear shooting method is proposed.
Proceedings ArticleDOI
Lazy Steering RRT*: An Optimal Constrained Kinodynamic Neural Network Based Planner with no In-Exploration Steering
TL;DR: A lazy-steering kinodynmaic RRT* is proposed in which the use of numerical methods is delayed until a potential collision free path has been found, and only then the numerical techniques are invoked, which results in a huge improvement in the run time with little trade off on optimality.
References
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Book
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Uri M. Ascher,Linda R. Petzold +1 more
TL;DR: This book is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications.
Journal ArticleDOI
A method for solving algebraic equations using an automatic computer
Journal ArticleDOI
On trust region methods for unconstrained minimization without derivatives
TL;DR: Algorithms for unconstrained minimization without derivatives that form linear or quadratic models by interpolation to values of the objective function are considered, because numerical experiments show that they are often more efficient than full quadRatic models for general objective functions.
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