<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">D. KUMAR</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A COLLOCATION SCHEME FOR SINGULAR BOUNDARY VALUE PROBLEMS ARISING IN PHYSIOLOGY</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34B16</style></keyword><keyword><style  face="normal" font="default" size="100%">65L10</style></keyword><keyword><style  face="normal" font="default" size="100%">65L12</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">24</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A new collocation method for the solution of a class of second-order two-point boundary value problems associated with physiology and other areas with a singular point at one endpoint is constructed. The singularity of the differential equation is modified by L’Hôpital’s rule and the boundary condition ${ y′(0)=0}$ . Quintic B-spline functions on equidistant collocation points are used to approximate the solution. The quasi-linearization technique is used to reduce a non-linear problem to a sequence of linear problems. The system obtained on discretization is transformed to the system of linear algebraic equations which is easy to be solved. It is proved that the proposed algorithm converges to a smooth approximate solution of the singular boundary value problems and the error estimates are given. To check the theory and to demonstrate the efficiency of the proposed method, several numerical illustrations from physical model problems have been carried out. To show the effectiveness of the proposed method comparisons with several existing methods has also been done.&lt;/p&gt;
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