4515165 Apparatus and method for detecting tumors : Rober Carroll assigned to energy conversion Devices Inc

Abstract

We give uniformly convergent splines difference scheme for singularly perturbed boundary value problemsby using splines fitted with delta sequence due to the very stiff nature of the problem under consideration. We prove the O(min(h2,ε2)) order of uniform convergence with respect to small parameter ε at nodes on uniform mesh and O(min(h,ε)) order of uniform global convergence with respect to the approximate solution given by S(x)=∑i=1NSΔi(x)H(xi-x) where H is the Heaviside function, which is the approximation for the closed form of the exact solution.