High order fitted operator numerical method for self-adjoint singular perturbation problems

We consider self-adjoint singularly perturbed two-point boundary value problems in conservation form. Highest possible order of uniform convergence for such problems achieved hitherto, via fitted operator methods, was one (see, e.g., [Doolan et al. Uniform numerical methods for problems with initial and boundary layers, Boole Press, Dublin, 1980], p. 121]). Reducing the original problem into the normal form and then using the theory of inverse monotone matrices, a fitted operator finite difference method is derived via the standard Numerov's method. The scheme thus derived is fourth order accurate for moderate values of the perturbation parameter whereas for very small values of this parameter the method is "-uniformly convergent with order two". Numerical examples are given in support of the theory. Article Outline

• Type: Journal
• Year: 2005
• Where: AMC
• Authors: Kailash C. Patidar
• Keywords: AMC 2005, Problems, Two-point Boundary Value, Uniform Numerical Methods