MODE: A modern ordinary differential equation solver for C++ and CUDA

Ordinary differential equations (ODE) are used to describe the evolution of one or more dependent variables using their derivatives with respect to an independent variable. They arise in various branches of natural sciences and engineering. We present a modern, efficient, performance-oriented ODE solving library built in C++20. The library implements a broad range of multi-stage and multi-step methods, which are generated at compile-time from their tableau representations, avoiding runtime overhead. The solvers can be instantiated and iterated on the CPU and the GPU using identical code. This work introduces the prominent features of the library with examples