High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the presented methods are efficient and applicable for lower and upper solutions.