Rough Differential Equation Solver

Introduction

This is the documentation for the projects RDE_lib2 and libalgebra-demo.

RDE_lib2 is the implementation of a numerical rough differential equation solver. Several rough paths are implemented, including Browian paths and fractional Brownian paths. RDE's driven by these paths are then solved in both the linear and non-linear case.

Libalgebra-demo provides the algebraic structure required.

The accompanying example project - RDE_Solver(example) - demonstrates RDE_lib2 and libalgebra-demo in action. The example project first solves the Landau-Lifschitz-Gilbert equation at time one, given a starting position. The example then solves a linear RDE driven by a fractional Brownian motion. As the name suggests, the example project is intended to demonstrate how the code can be used. The examples are straight forward implementations. We would strongly encourage users to change the driving paths, initial points and equations to explore the full scope of the project.

Libraries included with the distribution but not documented here are the following:

• Boost: http://www.boost.org/

• mkl: The Intel Math Kernel Library - http://software.intel.com/en-us/articles/intel-mkl/

• mpir: Multiple Precision Integers and Rationals - http://www.mpir.org/

• mtl_headers: Matrix Template Library - http://osl.iu.edu/research/mtl/

• SFMT: SIMD-oriented Fast Mersenne Twister (for random number generation) - http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/