A Galerkin Method for a Gaseous Ignition Model

We consider a Galerkin procedure to solve a parabolic integrodifferential equation that arises in a gas combustion model. This model has been proposed by Kassoy and Poland, and subsequently analyzed by Bebernes, Eberly and Bressan. The problem is formulated in the variational form. In order to estimate the error, some intermediate projection has been employed. Under certain conditions on the given data, the L^2 error estimate has been obtained. A fully descretized version by using an extrapolated Crank-Nicolson method has been applied and the order of convergence derived.