Volume 30, pp. 346-358, 2008.

Parameter-uniform fitted operator B-spline collocation method for self-adjoint singularly perturbed two-point boundary value problems

Mohan K. Kadalbajoo and Devendra Kumar

Abstract

In this paper, we develop a B-spline collocation method for the numerical solution of a self-adjoint singularly perturbed boundary value problem of the form $$-ϵ(a(x)y^{\prime }{)}^{\prime }+b(x)y(x)=f(x),a(x)\ge a^{\ast }>0,b(x)\ge b^{\ast }>0,a^{\prime }(x)\ge 0,y(0)=\alpha ,y(1)=\beta .$$ We construct a fitting factor and use the B-spline collocation method, which leads to a tridiagonal linear system. The method is analyzed for parameter-uniform convergence. Several numerical examples are reported which demonstrate the efficiency of the proposed method.

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Key words

B-spline collocation method, self-adjoint singularly perturbed boundary value problem, parameter-uniform convergence, boundary layer, fitted operator method

AMS subject classifications

34D15, 30E25, 20B40