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A novel algorithm for solving the ordinary differential equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Pleszczynski, Mariusz |
| Copyright Year | 2017 |
| Abstract | Development of the advanced computational software, including packages for symbolic computations, created new possibilities for solving the initial value problems for ordinary differential equations. The specific methods, that could be considered only theoretically without the possibility of symbolic computations, became particularly important. One of such methods is the method based on one of the fundamental theorems in mathematical analysis, known in the professional literature as the Taylor formula [?]grzy. Idea of this approach is very simple, but its application requires the calculation of the higher order derivatives of the discussed function which could cause the problems in times when the technique of symbolic computations with the use of digital machines was not yet available. These problems however disappear when we have such computer techniques at our disposal. Obviously, there exist a number of methods suitable for solving problems of the considered kind, like, for example, the whole group of Runge-Kutty methods [6, 7, 8, 9], or the, less known, Adomian decomposition method [1, 4]. In this paper we compare the effectiveness of the investigated method with the effectiveness of the sixth order Runge-Kutty method and the numerical method implemented in Mathematica software [2]. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://mat.polsl.pl/monografie/books%5Cspoem%5Cmono_spem_str_103-112.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
