Scientific Computing and Software

This book brings together six peer-reviewed contributions from the Go20 Conference on Scientific Computing and Software, held in Gozo, Malta, from May 19-23, 2025. The invitation-only conference is limited to twenty participants and uses a single program without parallel sessions, allowing extended presentations and discussion.

The chapters address high-order Lie derivatives using Taylor-series arithmetic in the ADTAYL package; set-based integration of differential equations on matrix Lie groups; spectral deferred correction combined with smooth Brownian bridge approximations for stochastic differential equations; spectral domain decomposition for singularly perturbed two-point boundary value problems; distributed parallelization strategies for particle-in-Fourier schemes in kinetic plasma simulation; and layer-parallel training for transformers using multigrid reduction in time.

A central theme is the connection between numerical analysis, software design, and computational implementation. The contributions examine mathematical structure, algorithmic accuracy, and computational performance. Numerical examples include a gantry crane model, three-dimensional matrix dynamics, test problems for stochastic differential equations, plasma benchmarks, and transformer training. These studies show how choices of formulation, discretization, and parallelization affect the behaviour of scientific software.

The volume is intended for researchers, practitioners, software developers, and graduate students in scientific computing, numerical analysis, and high-performance computing.