Computational approaches to initial-boundary value problems with Neumann boundary conditions

Solving Boundary Value Problems With Neumann Conditions Using Direct Method

In this paper, the direct method is utilized for solving second order two-point boundary value problem of Neumann type. The method will obtain the solution of the second order boundary value problem directly without reducing it to to first order equations. The method will be implemented using variable step size via shooting technique adapted with the Newton method. Numerical results are given t...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

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.

Nonlocal Problems with Neumann Boundary Conditions

We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition, we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probab...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...