## Abstract

The stochastic time-fractional equation ∂ _{t} Ψ - Δ∂ _{t} ^{1-α} Ψ = f + W˙ with space-time white noise W˙ is discretized in time by a backward-Euler convolution quadrature for which the sharp-order error estimate (E||Ψ(·, t _{n} ) - Ψ _{n} || _{ L 2 (O) } ^{2} )) ^{1/2} = O(τ ^{1/2 - αd/4} ) is established for α ∈ (0, 2/d), where d denotes the spatial dimension, Ψ _{n} the approximate solution at the nth time step, and E the expectation operator. In particular, the result indicates sharp convergence rates of numerical solutions for both stochastic subdiffusion and diffusion-wave problems in one spatial dimension. Numerical examples are presented to illustrate the theoretical analysis.

Original language | English |
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Pages (from-to) | 1715-1741 |

Number of pages | 27 |

Journal | Mathematics of Computation |

Volume | 88 |

Issue number | 318 |

DOIs | |

Publication status | Published - 1 Sept 2018 |

## Keywords

- Error estimates
- Space-time white noise
- Stochastic partial differential equation
- Time-fractional derivative

## ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics