Slides

AbstractBackgroundMain resultThe Runge–Kutta methodNumerical ExampleRecent developmentsAppendix/BackupOverall performance comparison:#Partition, #Dim, #Sample, and CPU time required for 10 −4 accuracy.Method #Partition #Dim #Sample CPU time (sec)E-M + MC 2000 4000 10 8 1.72 × 10 5E-M + Extrpltn + QMC 16 + 8 48 5× 10 6 1.27 × 10 2N-V + QMC 12 36 2 × 10 5 3.24N-V + Extrpltn + QMC 4 + 2 18 2× 10 5 1.76KNN + QMC 10 40 2 × 10 5 3.4KNN + Extrpltn + QMC 2 + 1 12 2× 10 5 1.2S. Ninomiya, M. Ninomiya Extension of a higher-order weak approximation