A high dimensional model representation based numerical method for solving ordinary differential equations |
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Authors: | Email author" target="_blank">Nejla?AltayEmail author Metin?Demiralp |
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Institution: | (1) Informatics Institute, Istanbul Technical University, 34469 Besiktas, Istanbul, Turkey |
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Abstract: | A new numerical method for solving ordinary differential equations by using High Dimensional Model Representation (HDMR) has
been developed in this work. Higher order ordinary differential equations can be reduced to a set of first order ODEs. Although
HDMR is generally used for multivariate functions, univariate functions are taken into account throughout the work because
of the ODEs’ natures. Not the numerical solution but its image under an appropriately chosen linear ordinary differential
operator is expressed as a linear combination of the positive deviation powers of independent variable from its initial value.
The linear combination of these image functions are expected to form a basis set under consideration. The unknown constants
in the linear combination are found by maximizing the constancy measurer formed in terms of the HDMR components after they
are evaluated. Results are compared with well-known step size based numerical methods. A semi qualitative error analysis of
the proposed method is also established. |
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