SeMA DOI 10.1007/s40324-017-0132-2 A robust numerical algorithm for solving singular boundary value problems in one space dimension by B-spline method Mohamed El-Gamel 1 · Neveen El-Shamy 1 · Waleed El-bashbashy 1 Received: 11 May 2017 / Accepted: 28 July 2017 © Sociedad Española de Matemática Aplicada 2017 Abstract This paper is concerned with the application of B-spline method to the numerical solution of singular time dependent problems. Error analysis is presented. The boundary value problems are reduced to a system of algebraic equations and Q–R method is used to establish numerical procedures. The method is thoroughly tested with the numerical results presented. The illustrative example confirm the validity of the method. Keywords B-spline · Singular · One space dimension · Numerical solution Mathematics Subject Classification 35k67 · 74H15 1 Introduction Accurate and fast numerical solution of two-point singular boundary value problems in ordinary differential equations is necessary in many important scientific and engineering applications, e.g. reactant concentration in a chemical reactor, boundary layer theory, control and optimization theory, and flow networks in biology, thermal distribution in human head, the study of astrophysics such as the theory of stellar interiors, the thermal behavior of a spherical cloud of gas, isothermal gas spheres, and the theory of thermionic currents. Recently, William and Pennline [34] and Pandey and Verma [22] , discussed existence and uniqueness of such type of singular two-point boundary value problems arising in chemical engineering. Krasnyk et al. [17], discussed higher order singularities in chemical process models. Our concern in this work is the derivation of the numerical solution based on B-spline method for the singular two-point boundary value problem B Mohamed El-Gamel gamel_eg@yahoo.com 1 Department of Mathematical Sciences, Faculty of Engineering, Mansoura University, Mansoura, Egypt 123