An invariant imbedding algorithm for the solution of inhomogeneous linear two-point boundary value problems

An algorithm is developed for the numerical solution of inhomogeneous linear twopoint boundary value problems using the method of invariant imbedding. The method handles the case in which the standard Riccati equation of the imbedding method fails to have a solution over the entire interval of interest. Very general sets of boundary conditions are imposed. While the development is for scalar problems only, all steps generalize readily to the case of matrix equations. An efficient program implementing the algorithm has been written and several examples are solved by the method. Some of these are of such a nature that more standard integration schemes provide unsatisfactory results.