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Classical and Quasi-Newton Methods for a Meteorological Parameters Prediction Boundary Value Problem |
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PP: 2683-2693 |
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Author(s) |
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Ioannis Famelis,
Georgios Galanis,
Matthias Ehrhardt,
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Abstract |
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We study the numerical solution of a Boundary Value problem for second order quadratic differential equations which arises
in the numerical prediction of meteorological parameters. In the present work, we use finite differences and focus on the numerical
solution of the resulting nonlinear system. More precisely, we apply classical Newton’s and Quasi-Newton methods paying attention to
the special sparse form of the Jacobian matrix and modify appropriately the LU factorization in order to reduce significantly the required
floating point operations. Furthermore, we implement and study in depth the behavior of all the proposed procedures in respect of their
accuracy, stability and complexity, using data from South East Mediterranean Sea. All the methods are tested with a variety of initial
values and their performance is presented and discussed leading to interesting results on the sensitivity of the selected starting point. |
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