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Variable Step Size Adams Methods for BSDEs

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  • Qiang Han
  • Mehmet Emir Koksal

Abstract

For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. It is deduced that the conditions of local truncation errors with respect to Y and Z reach high order. The coefficients in the numerical methods are inferred and bounded under appropriate conditions. A necessary and sufficient condition is given to judge the stability of our numerical schemes. Moreover, the high-order convergence of the schemes is rigorously proved. The numerical illustrations are provided.

Suggested Citation

  • Qiang Han & Mehmet Emir Koksal, 2021. "Variable Step Size Adams Methods for BSDEs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, December.
    • Handle: RePEc:hin:jjmath:9799627
    DOI: 10.1155/2021/9799627
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    Cited by:

    1. Pei Zhang & Nur Anisah Mohamed & Adriana Irawati Nur Ibrahim, 2023. "Mean-Field and Anticipated BSDEs with Time-Delayed Generator," Mathematics, MDPI, vol. 11(4), pages 1-13, February.

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