On the convergence of a fourth-order method for a class of singular boundary value problems

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...

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...

The variational iteration method for a class of tenth-order boundary value differential equations

A Note on Fourth Order Method for Doubly Singular Boundary Value Problems

We present a fourth order finite difference method for doubly singular boundary value problem p x y′ x ′ q x f x, y , 0 < x ≤ 1 with boundary conditions y 0 A or y′ 0 0 or limx→ 0p x y′ x 0 and αy 1 βy′ 1 γ , where α > 0 , β ≥ 0 , γ and A are finite constants. Here p 0 0 and q x is allowed to be discontinuous at the singular point x 0. The method is based on uniform mesh. The accuracy of the me...

On the existence of nonnegative solutions for a class of fractional boundary value problems

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...