The Galerkin method for singular nonoscillatory two-point boundary value problems

Abstract

The Galerkin method with special patch basis is used for the approximation of the solution of a general class of second order singular two-point boundary value problems. Convergence is analysed in several norms. Higher order convergence in the uniform norm are obtained for special data. The results are new both for special and general data. The class of problems treated in this dissertation extends the class of problems treated in the literature in many directions. The existence, uniqueness and the regularity of the solutions are not assumed; these are studied in proper places as needed. Both linear and nonlinear problems are treated in this dissertation.