A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity

and reducing the problem to one of iteratively solving a linear equation for un once the previous iterates have been determined. However, Adomian partitions (1.4) into a sequence of linear ODEs in either x or t whose solutions cannot generally be made to satisfy the boundary and initial conditions. Even when applied to an initial value problem with boundary conditions, the convergence of the solution depends sensitively on powers of f and its derivatives. In solving a similar problem in [1], Adomian must choose very specific initial data to guarantee local convergence in time. Our method arranges terms so that each linear problem is a PDE boundary value problem which is naturally solved with an expansion of eigenfunctions of ∂xx or a similar operator. We are able to show local convergence for any initial data f and global convergence given a suitable bound