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

In this paper, a new initial value method for solving a class of nonlinear singularly perturbed boundary value problems with a boundary layer at one end is proposed. The method is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). Using singular perturbation anal...

The numerical analysis of boundary layer effect is one of the major concerned problems in boundary element method (BEM). The accuracy of this problem depends on the precision of the evaluation of the nearly singular integrals. In the boundary element analysis with direct formulation, the hyper-singular integral will arise from the potential derivative boundary integral equations (BIEs). Thus th...

In this article, we establish the existence results for boundary value problems of the singular fractional differential systems. Our analysis relies on the well known Leray-Schauder nonlinear alternative theory. An example is presented to illustrate the main results. 2000 Mathematics Subject Classification: 92D25, 34A37, 34K15.

In this paper we study existence of positive solutions to singular elliptic boundary value problems involving divergence terms in general domains. By constructing suitable upper and lower solutions and making comparison, we obtain suucient conditions for existence and nonexistence of solutions. We also study a concrete example to show that the conditions imposed on parameters appearing in the s...

In this paper, we study the existence of positive solutions for nonlinear four-point singular boundary-value problems for higher-order equation with the p-Laplacian operator. Using the fixed-point index theory, we find conditions for the existence of one solution, and of multiple solutions.

In this paper, a novel method is proposed for solving nonlinear singular fourth order four-point boundary value problems (BVPs) by combining advantages of the homotopy perturbed method (HPM) and the reproducing kernel method (RKM). Some numerical examples are presented to illustrate the strength of the method. © 2011 Elsevier Ltd. All rights reserved.