Global convergence method for singularly perturbed boundary value problems

AbstractWe give uniformly convergent splines difference scheme for singularly perturbed boundary value problems(1)-εu″+p(x)u′+q(x)u=f(x),u(a)=α0,u(b)=α1,by 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