Journal ArticleDOI
Replacing the finite difference methods for nonlinear two-point boundary value problems by successive application of the linear shooting method
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TLDR
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.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2019-10-01. It has received 16 citations till now. The article focuses on the topics: Finite difference & Finite difference method.read more
Citations
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Journal ArticleDOI
Numerical and experimental study on temperature field reconstruction based on acoustic tomography
TL;DR: In this paper, a reconstruction model based on radial basis function approximation with polynomial reproduction is presented for solving the AT inverse problem, which considers the refraction effect of sound wave paths in the non-uniform temperature field.
Journal ArticleDOI
Least-squares solutions of boundary-value problems in hybrid systems
Hunter Johnston,Daniele Mortari +1 more
TL;DR: The proposed framework is used to solve the one-dimensional convection–diffusion equation to further highlight the utility of the Theory of Functional Connections outside of hybrid systems.
Journal ArticleDOI
Analysis of Reliable Solutions to the Boundary Value Problems by Using Shooting Method
TL;DR: In this paper , the authors used the shooting method to find numerical solutions to the boundary value problems of ODEs, and the convergence rate of the method to the exact solution was found to be high.
Posted Content
The Theory of Functional Connections: A journey from theory to application.
TL;DR: The theory of functional connections (TFC) as discussed by the authors is a general methodology for functional interpolation that can embed a set of user-specified linear constraints and can be leveraged to transform constrained optimization problems to unconstrained ones.
Journal Article
The Linearization Methods as a Basis to Derive the Relaxation and the Shooting Methods
István Faragó,Stefan M. Filipov +1 more
TL;DR: This work shows that relaxing a shooting trajectory, i.e. an initial value problem solution, is in fact a projection transformation, and demonstrates that the shooting methods can be derived from the linearization methods, too.
References
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Book
Numerical methods for ordinary differential equations
TL;DR: This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.
Journal ArticleDOI
Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix
Book
Quasilinearization and nonlinear boundary-value problems
Richard Bellman,Robert E. Kalaba +1 more
TL;DR: Quasilinearization and nonlinear boundary value problems as discussed by the authors, where the boundary value problem is formulated as a quadratic equation of the value of a boundary value.