The present report intends to deal with the spontaneous jet ignition, occurring just after the sudden outburst of hydrogen from a high-pressure reservoir into atmosphere. The propensity of hydrogen to ignite, is a complex problem, and little is known, in spite of numerous experiments and numerical analyses carried out. One possible scenario involves the effect of heat and mass diffusion at the contact surface, separating the cooled hydrogen from heated air, which may trigger chemistry and ultimately lead to ignition. A model with multistep kinetics for hydrogen-air combustion is examined here in the short time limit. A proper formulation has been developed by adding perturbation to the chemically frozen flow solution. A strategy for the numerical solution of the resulting linear problem involves splitting the problem into three subproblems. Results show two distinct regimes where early on, initiation is dominant, and at later times, chain-branching plays an important role.