Reactive molecular dynamics: numerical methods and algorithmic techniques. ..In this paper, we present implementation details of sPuReMD (serial Purdue reactive molecular dynamics program), a unique reactive classical MD code. We describe various data structures, and the charge equilibration solver at the core of the simulation engine. This Krylov subspace solver relies on a preconditioner based on incomplete LU factorization with thresholds (ILUT), specially targeted to our application. We comprehensively validate the performance and accuracy of sPuReMD on a variety of hydrocarbon systems. In particular, we show excellent per-time-step time, linear time scaling in system size, and a low memory footprint. sPuReMD is a freely distributed software with GPL and is currently being used to model diverse systems ranging from oxidative stress in biomembranes to strain relaxation in Si-Ge nanorods.