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A Legendre-based computational method for solving a class of Itô stochastic delay differential equations

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Abstract

This paper provides a numerical method for solving a class of Itô stochastic delay differential equations (SDDEs). The method’s novelty is its use of the spectral collocation approach using Legendre polynomials for solving SDDEs. We prove that the method is strongly convergent in L2 and proceed to demonstrate its computational efficiency and superior accuracy.

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Acknowledgments

We thank anonymous referees for several useful suggestions which helped improve the quality of this work.

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Authors and Affiliations

  1. Department of Statistics, Rice University, Houston, TX, 77005, USA

    Philip A. Ernst

  2. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran

    Fazlollah Soleymani

Authors
  1. Philip A. Ernst
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  2. Fazlollah Soleymani
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Correspondence to Philip A. Ernst.

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Ernst, P.A., Soleymani, F. A Legendre-based computational method for solving a class of Itô stochastic delay differential equations. Numer Algor 80, 1267–1282 (2019). https://doi.org/10.1007/s11075-018-0526-y

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  • DOI: https://doi.org/10.1007/s11075-018-0526-y

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