Solving a kind of BVP for second-order ODEs using novel data formats for dense matrices

Abstract

The aim of this paper is to show that a kind of boundary value problem for second-order ordinary differential equations which reduces to the problem of solving tridiagonal systems of linear equations can be efficiently solved on modern multicore computer architectures. A new method for solving such tridiagonal systems of linear equations, based on recently developed algorithms for solving linear recurrence systems with constant coefficients, can be easily vectorized and parallelized. Further improvements can be achieved when novel data formats for dense matrices are used.