تقرير
On approximate implicit Taylor methods for ordinary differential equations
| العنوان: | On approximate implicit Taylor methods for ordinary differential equations |
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| المؤلفون: | Baeza, Antonio, Bürger, Raimund, Martí, María del Carmen, Mulet, Pep, Zorío, David |
| المصدر: | Comput. Appl. Math. 39 (2020), no. 4, Paper No. 304, 21 pp |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a method that requires less evaluations of the function that defines the ODE and its derivatives than the usual version. On the other hand, an efficient numerical solution of the equation that arises from the discretization by means of Newton's method is introduced for an implicit scheme of any order. Numerical experiments illustrate that the resulting algorithm is simpler to implement and has better performance than its exact counterpart. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s40314-020-01356-8 |
| URL الوصول: | http://arxiv.org/abs/2402.01473 |
| رقم الأكسشن: | edsarx.2402.01473 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s40314-020-01356-8 |
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