Coleman’s theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage.

We present a unified framework in which to study splitting methods for polynomial vector fields in R. The vector field is to be represented as a sum of shears, each of which can be integrated exactly, and each of which is a function of k < n variables. Each shear must also inherit the structure of the original vector field: we consider Hamiltonian, Poisson, and volumepreserving cases. Each case...

Abstract In this work, a method is put forward to obtain the dynamic solution efficiently and accurately for large-scale train–track–substructure (TTS) system. It called implicit-explicit integration multi-time-step (abbreviated as m I- n E-MTS method). The TTS system divided into train–track subsystem substructure subsystem. Considering that root cause of low efficiency obtaining lies in solvi...

This investigation is concerned with the use of an implicit integration method with adjustable numerical damping properties in the simulations of flexible multibody systems. The flexible bodies in the system are modeled using the finite element absolute nodal coordinate formulation (ANCF), which can be used in the simulation of large deformations and rotations of flexible bodies. This formulati...

We look at adaptive time integration in the context of discontinuous Galerkin methods for the three dimensional unsteady compressible Navier-Stokes equations. Several explicit and implicit schemes will be compared. Philipp Birken, Gregor Gassner, Mark Haas and Claus-Dieter Munz