Integral Method with the Adomian Decomposition: Approximate Solution of the Liouville–Bratu–Gelfand Problem for a Cylindrical Space

A method of solving singular boundary-value problems on the basis of the combined use of the Adomian decomposition method and a special integral relation is presented. This method was used to advantage for approximate analytical solution of the problem on the thermal explosion in a cylindrical space, defined by the differential Liouville–Bratu– Gelfand equation with a Dirichlet boundary condition, and the numerical results of this solution have demonstrated the high efficiency of the indicated method. The errors of the approximate solutions obtained with it are smaller by as a minimum an order of magnitude than the errors of the solutions obtained on the basis of the classical Adomian decomposition method and other its related methods.