BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Nested Picard Iterative Integrators for the Dirac equation in the nonrelativistic limit Cai, Yongyong


We present the construction and analysis of uniformly accurate nested Picard iterative integrators (NPI) for the Dirac equation in the nonrelativistic limit involving a dimensionless parameter inversely proportional to the speed of light. To overcome the difficulty induced by the rapid temporal oscillation, we present the construction of several NPI methods which are uniformly first-, second- and third-order convergent in time. The NPI method can be extended to arbitrary higher order in time with optimal and uniform accuracy. The implementation of the second order NPI method will be demonstrated and analyzed.

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