A novel approach for the solution of a class of singular boundary value problems arising in physiology

Authors:
S. A. Khuri;A. Sayfy
Affiliations:
Department of Mathematics and Statistics, American University of Sharjah, United Arab Emirates;Department of Mathematics and Statistics, American University of Sharjah, United Arab Emirates
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

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Abstract

A new approach implementing a modified decomposition method in combination with the cubic B-spline collocation technique is introduced for the numerical solution of a class of singular boundary value problems arising in physiology. The domain of the problem is split into two subintervals; a modified decomposition procedure based on a special integral operator is implemented in the vicinity of the singular point and outside this domain the resulting boundary value problem is tackled by applying the B-spline scheme. Performance of this method is examined numerically; the examples reveal that the current approach converges to the exact solution rapidly and with O(h^2) accuracy. Results show that the method yields a numerical solution in very good agreement with the existing exact and approximate solutions.