except for the first and last subdomains, where in the Neumann step the Neumann conditions are replaced by homogeneous

Dirichlet conditions at the physical boundaries.

Schaefer, "Lower bounds for blow-up time in parabolic problems under

Dirichlet conditions," Journal of Mathematical Analysis and Applications, vol.

He proposed that the homogeneous

Dirichlet conditions may be satisfied exactly by representing the solution as the product of two functions: (1) an real-valued function that takes on zero values on the boundary points; and (2) an unknown function that allows to satisfy (exactly or approximately) the differential equation of the problem.

Considering the

Dirichlet conditions at x = 0 and x = [x.

This field satisfies the

Dirichlet conditions at all four sides.

where [GAMMA] symbolizes the boundary, and the

Dirichlet conditions are considered at 20[degrees]C for natural convective air-cooling BEM formulation, Green's function as a solution of the Equation (2) through (7) as follows.

The inhomogeneous polyanalytic equation is studied by Begehr and Kumar [28] in D with

Dirichlet conditions and the following result is obtained.

The system (11) is accompanied with the following time-independent

Dirichlet conditions1], these functional conditions include as a particular case, the

Dirichlet conditionsIn this case, the profile record builds sets of (x, y) points for each numerical method, where the x values are grid points, and the y values are relative elapsed time changes for mixed boundary conditions with respect to

Dirichlet conditions, changes in elapsed time for Neumann conditions with respect to

Dirichlet conditions, and relative changes in error for derivative conditions with respect to

Dirichlet conditions.

Dirichlet conditions are assumed on a closed subset [[GAMMA].

The Robin condition is consistent with the analysis in [11] where it is shown that

Dirichlet conditions on inflow are preferred as v approaches 0.