Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension
| العنوان: | Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension |
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| المؤلفون: | Metin Demiralp, Coşar Gözükirmizi |
| المصدر: | Journal of Mathematical Chemistry. 56:1826-1848 |
| بيانات النشر: | Springer Science and Business Media LLC, 2017. |
| سنة النشر: | 2017 |
| مصطلحات موضوعية: | 010304 chemical physics, Degree (graph theory), Computational complexity theory, Computer science, Applied Mathematics, Probabilistic logic, Recursion (computer science), 020206 networking & telecommunications, 02 engineering and technology, General Chemistry, Extension (predicate logic), Space (mathematics), 01 natural sciences, Algebra, Ordinary differential equation, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, Initial value problem |
| الوصف: | Probabilistic evolution theory facilitates the solution of initial value problem of explicit autonomous ordinary differential equations with second degree multinomial right hand side functions. Its formulation has components we call telescope matrices. The matrices grow in size very rapidly and has many zeroes and repeating structures. In order to avoid the computational complexity coming from telescope matrices, squarified telescope matrices are utilized. Their calculation is through a recursion. This recursion has been used in several works by the authors and their colleagues but its proof was not given. This work gives the proof of the recursion and all the surrounding details. A second purpose of this work is to provide a method for most facilitative (optimal) space extension. Space extension is needed for using probabilistic evolution theory when degree of multinomiality of the right hand side functions is more than two. For this purpose, an approach using method of exhaustion (brute-force) is proposed. |
| تدمد: | 1572-8897 0259-9791 |
| DOI: | 10.1007/s10910-017-0849-2 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::cd589e2d993debe8366288701b10a9f4 https://doi.org/10.1007/s10910-017-0849-2 |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi...........cd589e2d993debe8366288701b10a9f4 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15728897 02599791 |
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| DOI: | 10.1007/s10910-017-0849-2 |