A NEW SECOND-ORDER DIFFERENCE APPROXIMATION FOR NONLOCAL BOUNDARY VALUE PROBLEM WITH BOUNDARY LAYERS

Boundary Value Problem for Second-order Differential Operators with Mixed Nonlocal Boundary Conditions

In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...

Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions: Existence, Uniqueness, and Approximation

and Applied Analysis 3 In BVP 1.4 – 1.6 , it can be found that the boundary condition 1.5 is dependent on all the x a , x b , x′ a , and x′ b terms. First, existence and uniqueness of solutions of BVP 1.4 – 1.6 is established by combining the method of upper and lower solutions with LeraySchauder degree theory. Then, the general quasilinearization method is applied to construct the approximatio...

Second-Order Boundary Value Problem with Integral Boundary Conditions

A Novel Finite Difference Method of Order Three for the Third Order Boundary Value Problem in ODEs

In this article we have developed third order exact finite difference method for the numerical solution of third order boundary value problems. We constructed our numerical technique without change in structure of the coefficient matrix of the second-order method in cite{Pand}. We have discussed convergence of the proposed method. Numerical experiments on model test problems approves the simply...