Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. I: Arbitrariness and equipartition theorem in Kronecker power series

DOI10.1007/s10910-013-0298-5zbMath1298.34024OpenAlexW2071360066MaRDI QIDQ460871

Coşar Gözükırmızı, Metin Demiralp

Publication date: 9 October 2014

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-013-0298-5

zbMATH Keywords

dynamical systemsordinary differential equationsprobabilitypower seriesKronecker productsexpectation valueslinear algebra

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20)

Related Items (8)

Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension ⋮ Promenading in the enchanted realm of Kronecker powers: single monomial probabilistic evolution theory (PREVTH) in evolver dynamics ⋮ Somehow emancipating probabilistic evolution theory (PREVTH) from singularities via getting single monomial PREVTH ⋮ Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic ⋮ Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 2: Kernel separability, space extension, and, series solution via telescopic matrices ⋮ Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators. I: Integral representation of Kronecker power series and multivariate Hausdorff moment problems ⋮ Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators. II: The use of mathematical fluctuation theory ⋮ Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices

Cites Work

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• A probabilistic foundation for dynamical systems: phenomenological reasoning and principal characteristics of probabilistic evolution
• Probabilistic evolution approach for the solution of explicit autonomous ordinary differential equations. Part 2: Kernel separability, space extension, and, series solution via telescopic matrices
• High order closed Newton-Cotes exponentially and trigonometrically fitted formulae as multilayer symplectic integrators and their application to the radial Schrödinger equation
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• A probabilistic evolution approach trilogy. I: Quantum expectation value evolutions, block triangularity and conicality, truncation approximants and their convergence
• A probabilistic evolution approach trilogy. III: Temporal variation of state variable expectation values from Liouville equation perspective
• A probabilistic evolution approach trilogy. II: Spectral issues for block triangular evolution matrix, singularities, space extension

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