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The Numerical Study of Singularly Perturbed Differential-Difference Turning Point Problems: Twin Boundary Layers

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • P. Rai

    (Panjab University, Department of Mathematics (Center for Advance Study in Mathematics))

  • K. K. Sharma

    (Panjab University, Department of Mathematics (Center for Advance Study in Mathematics))

Abstract

A boundary value problem for singularly perturbed differential-difference equation with turning point is considered. Some a priori estimates are obtained on the solution and its derivatives. In general, to tackle such type of problems one encounters three difficulties: (i) due to presence of the turning point, (ii) due to presence of terms containing shifts and (iii) due to presence of the singular perturbation parameter. Due to presence of the singular perturbation parameter the classical numerical methods fail to give reliable numerical results and do not converge uniformly with respect to the singular perturbation parameter. In this paper a parameter uniform finite difference scheme is constructed to solve the boundary-value problem. A parameter uniform error estimate for the numerical scheme so constructed is established. Numerical experiments are carried out to demonstrate the efficiency of the numerical scheme and support the theoretical estimates.

Suggested Citation

  • P. Rai & K. K. Sharma, 2013. "The Numerical Study of Singularly Perturbed Differential-Difference Turning Point Problems: Twin Boundary Layers," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 285-292, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_31
    DOI: 10.1007/978-3-642-33134-3_31
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