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Approximate solution of random differential equation

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Differential Equations and Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1285))

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Abstract

Chebyshev method for solving random differential equation is presented. The convergence of the random coefficients of the Chebyshev series is established. Statistical properties of the random coefficients are discussed.

Research suppoted by U.S. Army Research Office, Grant No. DAAG-29-85-G-0109.

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References

  1. Bharucha-Reid, A. T. Approximate solution of random equations. North Holland, NY 1979.

    MATH  Google Scholar 

  2. Bharucha-Reid, A. T. and Sambandham, M. Random polynomials. Academic Press, FL, 1986.

    MATH  Google Scholar 

  3. Boyce, W. E. Approximate solution of random ordinary differential equations. Adv. Appl. Prob. 10 (1978) 172–184.

    Article  MathSciNet  MATH  Google Scholar 

  4. Klauder, J. R. and Petersen, W. P. Numerical integration of multiplicative-noise stochastic differential equations. SIAM J. Numer. Anal. 22 (1985) 1153–1166.

    Article  MathSciNet  MATH  Google Scholar 

  5. Kohler, W. E. and Boyce, W. E. A numerical analysis of some first order stochastic initial value problems. SIAM J. Appl. Math. 27 (1974) 167–179.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ladde, G. S. and Sambandham M. Stochastic versus deterministic. Math. Computer. Simul. 24 (1982) 507–514.

    Article  MathSciNet  MATH  Google Scholar 

  7. Ladde, G. S. and Sambandham, M Erro estimates of solutions and mean of solutions of stochastic differential systems. J. Math. Physics. 24 (1983) 815–822.

    Article  MathSciNet  Google Scholar 

  8. Ladde, G. S., Lakshmikantham, V. and Sambandham, M. Comparison theorems and error estimates of stochastic differential systems. Stoch. Anal. Appl. 3 (1985) 23–62.

    Article  MathSciNet  MATH  Google Scholar 

  9. Lax, M. D. Numerical solution of random nonlinear equations. Stoch. Anal. Appl. 3 (1985) 163–169.

    Article  MathSciNet  MATH  Google Scholar 

  10. Lax, M. D. "Approximate solution of random differential and integral." Applied stochastic Processes, G. Adomian, ed. Academic Press, NY 1980.

    Google Scholar 

  11. Nina-Mao Xia and Boyce, W. E. The density function of the solution of a random initial value problem containing small stochastic process. SIAM J. Appl. Math. 44 (1984) 1192–1209.

    Article  MathSciNet  MATH  Google Scholar 

  12. Rumelin, W. Numerical treatment of stochastic differential equations. SIAM J. Numer. Anal. 19 (1982) 604–613.

    Article  MathSciNet  Google Scholar 

  13. Sambandham, M., Srivatsan, T. and Bharucha-Reid, A. T. Numerical solution to singular integral equation in crack problems. Integiae Methods in Science and Engineening, ed. F. Payne, Hemisphere Publishers, NY, 1986, 130–148.

    Google Scholar 

  14. Sambandham, M., Christensen, M. J. and Bharucha-Reid, A. T. Numerical solution to singular integral equation III: Chebyshev polynomial and Fredholm equation of the second kind. Stoch. Anal. Appl. 3 (1985) 467–484.

    Article  MathSciNet  MATH  Google Scholar 

  15. Talay, D. "How to discretize stochastic differential equations." Nonlinean Filtering and Stochastic Contiol. Lecture Notes in Mathematics. Springer Verlag, NY (1980) Vol. 972, 276–292.

    Google Scholar 

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Ian W. Knowles Yoshimi Saitō

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© 1987 Springer-Verlag

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Sambandham, M., Medhin, N. (1987). Approximate solution of random differential equation. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080621

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  • DOI: https://doi.org/10.1007/BFb0080621

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18479-9

  • Online ISBN: 978-3-540-47983-3

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