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A novel approach for the solution of a class of singular boundary value problems arising in physiology. (English) Zbl 1201.65135
Summary: 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 $O\left({h}^{2}\right)$ accuracy. Results show that the method yields a numerical solution in very good agreement with the existing exact and approximate solutions.
##### MSC:
 65L60 Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE 92C30 Physiology (general)
##### References:
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