Solving ordinary differential equations on GPUs

Abstract

Ordinary Differential Equations (ODEs) are a fundamental mathematical tool to model physical, biological or chemical systems, and they are widely used in engineering, economics and social sciences. Given their vast appearance, it is of crucial importance to develop efficient numerical routines for solving ODEs that employ the computational power of modern GPUs. Here, we present a high-level approach to compute numerical solutions of ODEs by developing a generic implementation of the most common algorithms and combining this with modern C++ libraries like VexCL and Thrust. Our approach is based on generic programming and results in highly scalable and easy-to-use source code.