The convergence of \(\theta \)-Heun method for solving stochastic differential equations.

*(Chinese. English summary)*Zbl 1438.60097Summary: Heun method was an important numerical technique for solving stochastic differential equations. A new method based on Heun method was developed, known as the \(\theta \)-Heun method. The convergence of this method was examined. For scalar autonomous stochastic differential equations, when the two coefficients satisfied the linear growth condition and global Lipschitz condition, the order of its local convergence in mean was two, the order of its local convergence in mean square was one, and the order of its strong convergence square was one. Finally, the numerical solution obtained by \(\theta \)-Heun method was more approximate to analytical solution than Heun method, which was proved by numerical example.

##### MSC:

60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |

65C30 | Numerical solutions to stochastic differential and integral equations |