Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling
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Title
Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical ModelingDate
2018-11-27Publisher
MDPIISSN
2297-8747Bibliographic citation
Calatayud, J., Cortés, J. C., & Jornet, M. (2018). Some notes to extend the study on random non-autonomous second order linear differential equations appearing in mathematical modeling. Mathematical and Computational Applications, 23(4), 76.Type
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Abstract
The objective of this paper is to complete certain issues from our recent contribution
(Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear
differential equations: ... [+]
The objective of this paper is to complete certain issues from our recent contribution
(Calatayud, J.; Cortés, J.-C.; Jornet, M.; Villafuerte, L. Random non-autonomous second order linear
differential equations: mean square analytic solutions and their statistical properties. Adv. Differ. Equ.
2018, 392, 1–29, doi:10.1186/s13662-018-1848-8). We restate the main theorem therein that deals with
the homogeneous case, so that the hypotheses are clearer and also easier to check in applications.
Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of
mean square analytic solution and a numerical example. We also prove the uniqueness of mean
square solution via a habitual Lipschitz condition that extends the classical Picard theorem to mean
square calculus. In this manner, the study on general random non-autonomous second order linear
differential equations with analytic data processes is completely resolved. Finally, we relate our
exposition based on random power series with polynomial chaos expansions and the random
differential transform method, the latter being a reformulation of our random Fröbenius method. [-]
Is part of
Mathematical and Computational Applications, Vol.23, Iss. 4 (December 2018)Funder Name
Ministerio de Economía y Competitividad | Universitat Politècnica de València
Project code
MTM2017-89664-P
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Programa de Ayudas de Investigación y Desarrollo (PAID)
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- MAT_Articles [761]
- INIT_Articles [751]
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