A Simplified Milstein Scheme for SPDEs with Multiplicative Noise

Table 1

Runtime (seconds) for one path simulation using three methods 𝑌^𝑁_𝑁³, 𝑌^𝑁_𝑁², and 𝑌^𝑁_𝑁2 for 𝑁 = 64, 128, 256, 512, 1024.

𝑁	Implicit Euler scheme	Milstein scheme	Simplified Milstein scheme
64	38.316292	0.703536	0.690610
128	381.021714	3.628195	3.581998
256	3874.629760	19.811083	19.405515
512	46885.088426	126.663048	124.849040
1024	5.1574𝑒+005	842.699400	834.842365