Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods

The Existence and Behavior of Solutions for Nonlocal Boundary Problems

The existence of solutions for quasilinear parabolic equation with boundary conditions and initial conditions can be discussed by maximal regularity, and more and more works on this field show that the maximal regularity method is efficient. Here we will use some of recently results developed by H. Amann to investigate a specific boundary value problems and then apply the existence theorem to t...

Uniqueness of Solutions for Fourth-order Nonlocal Boundary Value Problems

Uniqueness implies uniqueness relationships are examined among solutions of the fourth-order ordinary differential equation, y (4) = f (x, y, y , y , y), satisfying 5-point, 4-point, and 3-point nonlocal boundary conditions. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reproduction in any medium, pr...

Equidistribution grids for two-parameter convection–diffusion boundary-value problems

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...

Positive Solutions of Some Higher Order Nonlocal Boundary Value Problems

We show how a unified method, due to Webb and Infante, of tackling many nonlocal boundary value problems, can be applied to nonlocal versions of some recently studied higher order boundary value problems. In particular, we give some explicit examples and calculate the constants that are required by the theory.

Positive Solutions of Some Nonlocal Boundary Value Problems