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Cubically convergent method for solving a standard boundary value problem

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PL
The paper presents a cubically convergent method for solving a standard boundary value problem consisting of n coupled first-order differential equations and n boundary conditions. The idea of the presented method is based on the shooting method using the expansion of the desired function into Taylor’s series including second-order derivatives. Effective use of the iteration formula requires introduction of sensitivity functions and their derivatives. In each iteration, the initial problem, composed of n(1+ n1+ n21 ) first-order differential equations, must be solved, where n1 signifies the number of unknown parameters. The convergence of the presented method has been illustrated on an example.
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2015-04-23
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bwmeta1.element.ojs-nameId-6e3e8ea9-5a94-37a7-828b-e6cd5da23db6-year-2015-article-1825
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