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Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function

Author

Listed:
  • Cortés, J.-C.
  • Navarro-Quiles, A.
  • Romero, J.-V.
  • Roselló, M.-D.

Abstract

This paper deals with the approximate computation of the first probability density function of the solution stochastic process to second-order linear differential equations with random analytic coefficients about ordinary points under very general hypotheses. Our approach is based on considering approximations of the solution stochastic process via truncated power series solution obtained from the random regular power series method together with the so-called Random Variable Transformation technique. The validity of the proposed method is shown through several illustrative examples.

Suggested Citation

  • Cortés, J.-C. & Navarro-Quiles, A. & Romero, J.-V. & Roselló, M.-D., 2018. "Solving second-order linear differential equations with random analytic coefficients about ordinary points: A full probabilistic solution by the first probability density function," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 33-45.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:33-45
    DOI: 10.1016/j.amc.2018.02.051
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    Cited by:

    1. Juan-Carlos Cortés & Ana Navarro-Quiles & José-Vicente Romero & María-Dolores Roselló, 2020. "Solving Second-Order Linear Differential Equations with Random Analytic Coefficients about Regular-Singular Points," Mathematics, MDPI, vol. 8(2), pages 1-19, February.

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