We study an explicit exponential scheme for the time discretisation of stochastic SchrS- dinger Equations Driven by additive or Multiplicative It6 Noise. The numerical scheme is shown to converge with strong order 1 i...We study an explicit exponential scheme for the time discretisation of stochastic SchrS- dinger Equations Driven by additive or Multiplicative It6 Noise. The numerical scheme is shown to converge with strong order 1 if the noise is additive and with strong order 1/2 for multiplicative noise. In addition, if the noise is additive, we show that the exact solutions of the linear stochastic Sehr6dinger equations satisfy trace formulas for the expected mass, energy, and momentum （i. e., linear drifts in these quantities）. Furthermore, we inspect the behaviour of the numerical solutions with respect to these trace formulas. Several numerical simulations are presented and confirm our theoretical results.展开更多
文摘We study an explicit exponential scheme for the time discretisation of stochastic SchrS- dinger Equations Driven by additive or Multiplicative It6 Noise. The numerical scheme is shown to converge with strong order 1 if the noise is additive and with strong order 1/2 for multiplicative noise. In addition, if the noise is additive, we show that the exact solutions of the linear stochastic Sehr6dinger equations satisfy trace formulas for the expected mass, energy, and momentum （i. e., linear drifts in these quantities）. Furthermore, we inspect the behaviour of the numerical solutions with respect to these trace formulas. Several numerical simulations are presented and confirm our theoretical results.
