Discretization of second-order ordinary differential equations with symmetries
| العنوان: | Discretization of second-order ordinary differential equations with symmetries |
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| المؤلفون: | V. A. Dorodnitsyn, E. I. Kaptsov |
| المصدر: | Computational Mathematics and Mathematical Physics. 53:1153-1178 |
| بيانات النشر: | Pleiades Publishing Ltd, 2013. |
| سنة النشر: | 2013 |
| مصطلحات موضوعية: | Examples of differential equations, Stochastic partial differential equation, Computational Mathematics, Collocation method, Mathematical analysis, Delay differential equation, Differential algebraic equation, Numerical partial differential equations, Mathematics, Integrating factor, Separable partial differential equation |
| الوصف: | A number of publications (indicated in the Introduction) are overviewed that address the group properties, first integrals, and integrability of difference equations and meshes approximating second-order ordinary differential equations with symmetries. A new example of such equations is discussed in the overview. Additionally, it is shown that the parametric families of invariant difference schemes include exact schemes, i.e., schemes whose general solution coincides with the corresponding solution set of the differential equations at mesh nodes, which can be of arbitrary density. Thereby, it is shown that there is a kind of mathematical dualism for the problems under study: for a given physical process, there are two mathematical models: continuous and discrete. The former is described by continuous curves, while the latter, by points on these curves. |
| تدمد: | 1555-6662 0965-5425 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::15aff8291c34383dd06b3af46d669bc2 https://doi.org/10.1134/s0965542513080058 |
| حقوق: | CLOSED |
| رقم الأكسشن: | edsair.doi...........15aff8291c34383dd06b3af46d669bc2 |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 15556662 09655425 |
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