Abstract
One-dimensional singularly-perturbed two-point boundary-value problems arising in various fields of science and engineering (for instance, fluid mechanics, quantum mechanics, optimal control, chemical reactor theory, aerodynamics, reaction-diffusion processes, geophysics, etc.) are treated. Either these problems exhibits boundary layer(s) at one or both ends of the underlying interval or they possess oscillatory behavior depending on the nature of the coefficient of the first derivative term. Some spline difference schemes are derived for these problems using splines in compression and splines in tension. Second-order uniform convergence is achieved for both kind of schemes. By making use of the continuity of the first-order derivative of the spline function, a tridiagonal system is obtained which can be solved efficiently by well-known algorithms. Numerical examples are given to illustrate the theory.
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Kadalbajoo, M., Patidar, K. Spline Techniques for the Numerical Solution of Singular Perturbation Problems. Journal of Optimization Theory and Applications 112, 575–594 (2002). https://doi.org/10.1023/A:1017968116819
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DOI: https://doi.org/10.1023/A:1017968116819