A uniformly convergent finite difference scheme for a singularly perturbed semilinear equation
SIAM Journal on Numerical Analysis
A spline method for second-order singularly perturbed boundary-value problems
Journal of Computational and Applied Mathematics
A recent survey on computational techniques for solving singularly perturbed boundary value problems
International Journal of Computer Mathematics
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We give uniformly convergent splines difference scheme for singularly perturbed boundary value problems -εu'' + p(x)u' + q(x)u = f(x), u(a) = α0, u(b) = α1 (1) 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) = Σi = 1N SΔi(x)H(xi-x) where H is the Heaviside function, which is the approximation for the closed form of the exact solution.