Milstein-type semi-implicit split-step numerical methods for non-linear stochastic differential equations with locally lipschitz drift terms

Burhaneddin Izgi, Coskun Cetin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We develop Milstein-type versions of semi-implicit split-step methods for numerical solutions of non-linear stochastic differential equations with locally Lipschitz coefficients. Under a one-sided linear growth condition on the drift term, we obtain some moment estimates and discuss convergence properties of these numerical methods. We compare the performance of multiple methods, including the backward Milstein, tamed Milstein, and truncated Milstein procedures on non-linear stochastic differential equations including generalized stochastic Ginzburg-Landau equations. In particular, we discuss their empirical rates of convergence.

Original languageEnglish
Pages (from-to)S1-S12
JournalThermal Science
Volume23
DOIs
Publication statusPublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 Society of Thermal Engineers of Serbia.

Keywords

  • Milstein method
  • Non-linear stochastic differential equations
  • Semi implicit split-step method

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