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During the period covered by this report we continued our research on the development and application of numerical methods for singularly-perturbed (or stiff) boundary value problems for ordinary differential equations and initial-boundary value problems for partial differential equations. Results were obtained for collocation methods for vector systems of two-point boundary value problems and for adaptive grid finite element methods for partial differential equations. We are applying our methods to several interesting physical problems, such as, the deformation of nonlinear elastic beams and a nonlinear Schrodinger equation which exhibits self focusing. (Author)