# Variable-mesh difference scheme for singularly-perturbed boundary-value problems using splines

@article{Kadalbajoo1996VariablemeshDS,
title={Variable-mesh difference scheme for singularly-perturbed boundary-value problems using splines},
author={Mohan K. Kadalbajoo and Rajesh K. Bawa},
journal={Journal of Optimization Theory and Applications},
year={1996},
volume={90},
pages={405-416}
}
AbstractA second-order variable-mesh difference scheme via cubic splines for singularly-perturbed boundary-value problems of the form $$y'' = \rho (x)y' + q(x)y + r(x), y(a) = a_0 , y(b) = a_1 ,$$ is presented. The convergence analysis is given and the method is shown to have quadratic convergence. Several test examples are solved to demonstrate the efficiency of the method.

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