This paper presents a new high-performance technique to parallelise numeric integration of large VLSI interconnect analog models on a general purpose GPU. The technique is based on the combination of space-state formulation with an explicit integration method based on the Adams-Bashforth second order formula. The paper studies the stability of the variable step explicit method and proposes a technique to guarantee integration stability specifically for interconnect systems. Although explicit methods require smaller integration steps compared to those of the traditional implicit techniques, they avoid the complex calculations inherent to implicit integration. The proposed approach is demonstrated using an RC VLSI interconnect model and results are compared to those achieved by Ngspice, a state-of-the-art implicit integration solver, implemented on the same parallel hardware. The results show that the speed-up of the parallelised explicit solution reaches one order of magnitude for large systems and is increasing with the circuit size.