Alternating direction implicit methods for two-dimensional diffusion with a non-local boundary condition

A new second-order finite difference technique based upon the Peaceman and Rachford (P - R) alternating direction implicit (ADI) scheme, and also a fourth-order finite difference scheme based on the Mitchell and Fairweather (M - F) ADI method, are used as the basis to solve the two-dimensional time dependent diffusion equation with non-local boundary conditions. The results of numerical experiments for these new methods are presented. These schemes use less central processor time (CPU) than a second-order fully implicit scheme based on the classical backward time centered space (BTCS) method for two-dimensional diffusion. They also have a larger range of stability than a second-order fully explicit scheme based on the classical forward time centered space (FTCS) method.

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