Fractional step methods for parabolic equations with a non-standard condition

摘要

The number of physical phenomena modelled by partial differential equations involving non-linear integral terms is constantly increasing. These terms may appear in the boundary conditions or in the governing equation itself. In the present report the integral term appears in the boundary conditions. An alternating direction implicit finite difference technique, which requires the solution of three tridiagonal sets of equations at each time step, is derived for solving the three-dimensional diffusion equation. The proposed scheme is computationally efficient and easy to implement. The new developed method is tested on a problem. The results of numerical testing show that the numerical method based on the finite difference technique discussed in the present paper produce good results.