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01-Applied Mathematics & Information Sciences
An International Journal
               
 
 
 
 
 
 
 
 
 
 
 
 
 

Content
 

Volumes > Volume 08 > No. 6

 
   

Classical and Quasi-Newton Methods for a Meteorological Parameters Prediction Boundary Value Problem

PP: 2683-2693
Author(s)
Ioannis Famelis, Georgios Galanis, Matthias Ehrhardt,
Abstract
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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