PMIRKDC: a parallel mono-implicit Runge-Kutta code with defect control for boundary value ODEs

We describe parallel software, PMIRKDC, for solving boundary value ordinary differential equations (BVODEs). This software is based on the package, MIRKDC, which employs monoimplicit Runge-Kutta schemes within a defect control algorithm. The primary computational costs involve the treatment of large, almost block diagonal (ABD) linear systems. The most significant feature of PMIRKDC is the replacement of sequential ABD software, COLROW, with new parallel ABD software, RSCALE, based on a parallel block eigenvalue rescaling algorithm. Other modifications involve parallelization of the setup of the ABD systems and solution interpolants, and defect estimation. Numerical results show almost linear speedups.