A.S.V. Ravi Kanth

Cubic spline for a class of singular two-point boundary value problems

In this paper we have presented a method based on cubic splines for solving a class of singular two-point boundary value problems. The original differential equation is modified at the singular point then the boundary value problem is treated by using cubic spline approximation. The tridiagonal system resulting from the spline approximation is efficiently solved by Thomas algorithm. Some model problems are solved, and the numerical results are compared with exact solution.

Cubic spline polynomial for non-linear singular two-point boundary value problems

We present a cubic spline polynomial for the solution of non-linear singular two-point boundary value problems. The quesilinearization technique is used to reduce the non-linear problem to a sequence of linear problems. The resulting sets of differential equations are modified at the singular point and are treated by using cubic spline for finding the numerical solution. The method is tested on three physical model problems from the literature.

A numerical method for singular two point boundary value problems via Chebyshev economizition

In this paper we present a numerical method for solving a two point boundary value problem in the interval [0,1] with regular singularity at x=0. By employing the Chebyshev economizition on [0,@d], where @d is near the singularity, we first replace it by a regular problem on some interval [@d,1]. The stable central difference method is then employed to solve the problem over the reduced interval. Some numerical results are presented to demonstrate the applicability of the method.

A numerical method for solving two-point boundary value problems over infinite intervals

In this paper we present a numerical method for the solution of a two-point boundary value problem posed on an infinite interval involving a second order linear differential equation. By reducing the infinite interval to a finite interval that is large and imposing approximate asymptotic boundary condition at the far end, the resulting boundary value problem is treated by using fourth order finite difference method. The stability of the method is analyzed and the theory is illustrated by solving test examples.

The method of inner boundary condition for singular boundary value problems

A method of inner boundary condition is presented for solving two-point singular boundary value problem. The original interval is divided into two parts. An inner boundary condition is obtained by using a series solution. Then, a special finite difference method of order two is employed to solve the problem in the interval [@d,1]. The method is implemented on several numerical examples and results are compared with exact solutions.

Computer Oriented Process for Treating Second Order Differential Equations with Singular Coefficient at the First Derivative Term

This paper applies the computer oriented process for solving second order differential equations with singular coefficient at the first derivative term. The original differential equation is modified at the singular point and then the differential equation is treated by using spline in tension. To test the efficiency of the proposed method both homogeneous and non-homogeneous singular boundary value problems are considered.