Adjoint System in the Shooting Method to Solve Boundary Value Problems
Ernest Scheiber
TL;DR
This paper introduces an approach using the adjoint system within the shooting method to improve solutions of boundary value problems, integrating Newton-Kantorovich iterations for enhanced accuracy.
Contribution
It presents a novel integration of the adjoint differential system into the shooting method, enabling more effective initial value approximations for boundary value problems.
Findings
Enhanced accuracy in boundary value problem solutions.
Effective use of adjoint systems for initial value estimation.
Integration of Newton-Kantorovich iterations improves convergence.
Abstract
The shooting method is used to solve a boundary value problem with separated and explicit constraints. To obtain approximations of an unknown initial values there are considered arguments based on the adjoint differential system attached to the given differential system. Finally the Newton - Kantorovich iterations are regained.
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Taxonomy
TopicsIterative Methods for Nonlinear Equations · Advanced Computational Techniques in Science and Engineering