Solution of the Two-Dimensional Second-Order Diffusion Equation With Nonlocal Boundary Condition

Abstract

In the mathematical modeling of many physical phenomena, the diffusion equations with nonlocal boundary condition can be appeared. In this paper, we focus on the two-dimensional inhomogeneous diffusion equations subject to a nonlocal boundary condition. We transform the model of partial differential equation (PDE) into a system of first order, linear, ordinary differential equations (ODEs).

Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions

“…A periodic boundary condition is combined with Dirichlet and Neumann boundary conditions [14], and it is set to isolate repeating temperature distribution in the solution's domain [15]. The periodic boundary condition, a special case of the nonlocal boundary [16] condition, is used in the present investigation. Generally, the periodic boundary condition is often employed in numerical simulations and mathematical models.…”

“…This method supports second order accuracy in the spatial grid sizes and first order time grid size. The explicit finite scheme has a restriction of determining time step The periodic boundary condition, a special case of the nonlocal boundary [16] condition, is used in the present investigation. Generally, the periodic boundary condition is often employed in numerical simulations and mathematical models.…”

Analytical and Numerical Investigation of two-dimensional Heat Transfer with Periodic Boundary Conditions

“…A special case of the nonlocal boundary [16] condition, the periodic boundary condition, is used in present investigation. Generally, periodic boundary condition is often used in numerical simulations and mathematical models.…”

An Efficient Numerical Technique for Solving Heat Equation With Nonlocal Boundary Conditions

“…The results presented that the above described method contain L-acceptable as well as fth order accuracy [23]. Soltanalizadeh [1,19] introduced the new technique of matrix formulation for the system of equations and he focused on the wave equation with the NLBC [5]. Mardan et al developed a hybrid numerical methods which is partially sixth-order accuracy in time and space, due to a combination of sixth-order nite approximations and fth-order Pade approximation.…”