Metaprogramming Applied to Numerical Problems

TL;DR

This paper demonstrates how C++ template metaprogramming can be effectively applied to implement a generic Runge-Kutta scheme, leading to improved performance in solving ordinary differential equations.

Contribution

It introduces a novel application of template metaprogramming to numerical methods, specifically for solving differential equations efficiently.

Findings

Template metaprogramming enables faster numerical computations.

The generic Runge-Kutta implementation outperforms classical methods.

Significant performance improvements are achieved through this approach.

Abstract

From the discovery that the template system of C++ forms a Turing complete language in 1994, a programming technique called Template Metaprogramming has emerged that allows for the creation of faster, more generic and better code. Here, we apply Template Metaprogramming to implement a generic Runge-Kutta scheme that can be used to numerically solve ordinary differential equations. We show that using Template Metaprogramming results in a significantly improved performance compared to a classical implementation.