Automatic integration of Euler-Lagrange equations with constraints. (English) Zbl 0576.65072
Numerical difficulties in the integration of some differential-algebraic equations, typically the Euler-Lagrange equations with constraints are discussed. After the introduction of the global index for such equations, a technique for reducing their index from three to two is given and it is shown that variable-order variable-step BDF methods converge for these index two problems. Careful consideration for the error is required because of the implicitness of the algebraic variables. Then, it is possible to organize the calculation so that only the algebraic variables are handled implicitly, while the differential variables are handled with a conventional predictor-corrector iteration of BDF.
Reviewer: T.Mitsui
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 70H03 | Lagrange’s equations |
| 65Yxx | Computer aspects of numerical algorithms |
| 34B30 | Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) |
Keywords:
automatic integration; constraints; backward differentiation; formula; differential-algebraic equations; Euler-Lagrange equations; global index; variable-order variable-step BDF methods; predictor-corrector iterationReferences:
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