Journal of the
Korean Mathematical Society JKMS

In this paper, we present a new method for solving a nonlinear two-point boundary value problem with finitely many singularities. Its exact solution is represented in the form of series in the reproducing kernel space. In the mean time, the $n$-term approximation $u_{n}(x)$ to the exact solution $u(x)$ is obtained and is proved to converge to the exact solution. Some numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method are compared with the exact solution of each example and are found to be in good agreement with each other.

Keywords: exact solution, singular nonlinear boundary value problem, reproducing kernel

MSC numbers: 34B16, 46E22, 47B32