The non-polynomial spline method is proposed to solve a singular boundary value problems. Some model problems are solved and the numerical results are compared with B-spline approximation and the exact solution. Results obtained by the method indicate the method is simple and effective. Key–Words: Singular point; Singular two-point boundary value problems; Cubic spline

We consider stagnation point flow away from a wall for creeping flow of dilute polymer solutions. For a simplified flow geometry, we explicitly show that a narrow region of strong polymer extension (a birefringent strand) forms downstream of the stagnation point in the UCM model and extensions, like the FENE-P model. These strands are associated with the existence of an essential singularity in...

This paper investigates the analytical approximate solutions of singular fourth order four-point boundary value problems using reproducing kernel method (RKM). The solution obtained by using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve singular fourth order four-point boundary value p...

This paper investigates the evaluation of the sensitivity, with respect to tangential perturbations of the singular point, of boundary integrals having either weak or strong singularity. Both scalar potential and elastic problems are considered. A proper definition of the derivative of a strongly singular integral with respect to singular point perturbations should accommodate the concomitant p...

An algorithm is described for the efficient numerical solution of singular two-point boundary value problems. The algorithm is based on collocation at Gauss points, is applied directly to second order equations and uses a transformation of the independent variable to obtain extra smoothness if needed. Numerical comparisons between a code based on this approach and codes based on other options w...

In this article, we develop the Sinc-Galerkin method based on double exponential transformation for solving a class of weakly singular nonlinear two-point boundary value problems with nonhomogeneous boundary conditions. Also several examples are solved to show the accuracy efficiency of the presented method. We compare the obtained numerical results with results of the other existing methods in...