Numerical Solution of a Turning Point Problem

The numerical values of the nodal points for the Sturm-Liouville equation with one turning point

An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established a...

On the Infinite Product Representation of Solution and Dual Equation of Sturm-Liouville Equation with Turning Point of Order 4m+1

Numerical method for a system of second order singularly perturbed turning point problems

In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...

On Numerical Solution of a Turning Point Problem

A numerical method for a singular perturbation problem with a turning point is considered. The method uses non-equidistant discretization meshes. The first order accuracy, uniform in the perturbation parameter is proved in the discrete L1 norm.

F-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM

We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed ...