On a Constructive Approach for Derivative-Dependent Singular Boundary Value Problems

On a Constructive Approach for Derivative-Dependent Singular Boundary Value Problems

A novel technique for a class of singular boundary value problems

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

Applying Legendre Wavelet Method with Regularization for a Class of Singular Boundary Value Problems

In this paper Legendre wavelet bases have been used for finding approximate solutions to singular boundary value problems arising in physiology. When the number of basis functions are increased the algebraic system of equations would be ill-conditioned (because of the singularity), to overcome this for large $M$, we use some kind of Tikhonov regularization. Examples from applied sciences are pr...

Boundary Value Problems with Singular Boundary Conditions

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions properties of the spectrum are studied and the completeness of the system of root functions is proved.

Multiple Positive Solutions for Singular Boundary-value Problems with Derivative Dependence on Finite and Infinite Intervals

In this paper, Krasnoselskii’s theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals.