On using cubic spline for the solution of problems in calculus of variations (Q342868)
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scientific article; zbMATH DE number 6654598
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On using cubic spline for the solution of problems in calculus of variations |
scientific article; zbMATH DE number 6654598 |
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On using cubic spline for the solution of problems in calculus of variations (English)
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18 November 2016
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The author discusses using cubic splines for the solution of problems in calculus of variations. The author recalls some definitions and theorems from \textit{B. Dacorogna} [Introduction to the calculus of variations. Transl. from the French. River Edge, NJ: World Scientific (2004; Zbl 1095.49002)] to state the existence and uniqueness of solutions. The author converts the original problem to a boundary value problems, then by defining special end conditions for cubic spline, a method of order \(O(h^{4})\) is derived and its convergence is presented in detail. A direct method based on cubic splines and Gauss-Legendre integration is developed. Theoretical orders of convergence are verified numerically using the data.
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calculus of variations
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collocation
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direct and indirect methods
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optimal convergence
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superconvergence
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Euler-Lagrange equation
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numerical examples
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cubic spline
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Gauss-Legendre integration
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