An Iterated, Multipoint Differential Transform Method

This paper makes three novel contributions: First, a concept for constructing veriably-self-co nsistent numerical evolution schemes for partialdierential-equat ion (PDE) initial-value problems (IVPs) is presented. Second, an iterated, multipoint dierential transform method (IMDTM) for numerically evolving PDE IVPs is presented. The IMDTM can be used to eciently implement veriably-self-co nsistent PDE evolution. Lastly, in order to eciently implement the IMDTM scheme, a generalized nitedierence stencil formula is derived which can take advantage of multiple higher-order spatial derivatives when computing even-higher-order derivatives. As is demonstrated, the performance of these techniques compares favorably to other explicit evolution schemes in terms of speed, memory footprint and accuracy.