On the fourth order PI equation and coalescing phenomena of nonlinear turning points

The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

Comparison of Diagnostic Value of Cast Analyzer X Iranian Software versus Curve Expert Software for Arch Form Construction based on Mathematical Models

  Objective: For the assessment of primary arch form, different methods have been used including qualitative classifications, inter-canine and inter-molar widths and quantitative and numerical methods using mathematical models. The purpose of this study was to compare the validity and reliability of Cast Analyzer X Iranian software with those of Curve Expert Professional version 1.1 for arch fo...

On the determination of asymptotic formula of the nodal points for the Sturm-Liouville equation with one turning point

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

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