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The numerical solution of random initial-value problems

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  • Harlow, D.G.
  • Delph, T.J.

Abstract

We outline a numerical technique for the solution of systems of nonlinear ordinary differential equations containing arbitrary numbers of random parameters and random initial conditions. The random parameters are restricted to be time-independent, and hence, stochastic processes are excluded from consideration. Depending upon the number of random initial conditions and parameters relative to the number of dependent variables, this technique yields either the joint probability density function for the dependent variables or the marginal probability density functions for individual dependent variables.

Suggested Citation

  • Harlow, D.G. & Delph, T.J., 1991. "The numerical solution of random initial-value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 33(3), pages 243-258.
    • Handle: RePEc:eee:matcom:v:33:y:1991:i:3:p:243-258
    DOI: 10.1016/0378-4754(91)90122-J
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    Cited by:

    1. Ladde, G.S. & Lawrence, Bonita A., 2003. "On joint probability density functions of discrete time iterative processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(6), pages 629-650.
    2. Griffin, Byron L. & Ladde, G.S., 2004. "Qualitative properties of stochastic iterative processes under random structural perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(3), pages 181-200.
    3. Zavattaro, M.G. & Riganti, R., 1992. "Statistics of the solution of singularly perturbed systems with random initial conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(5), pages 487-499.

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