Block Nyström type integrator for Bratu's equation

In this paper, we use a Block Nyström Method (BNM) to obtain the numerical solution for one-dimensional Bratu's problem. The convergence analysis of the method is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The accuracy benefit of the BNM is demonstrated by comparing it to several other known methods given in the literature. It is demonstrated that the BNM can also be used to solve Bratu's problem associated with initial conditions by simply adjusting the boundary conditions in the algorithm.