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The new alternating direction implicit difference methods for solving three-dimensional parabolic equations. (English) Zbl 1185.65151
Summary: A new alternating direction implicit (ADI) scheme for solving three-dimensional parabolic equations with nonhomogeneous boundary conditions is presented. The scheme is also extended to high-order compact difference scheme. Both of them have the advantages of unconditional stability and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and uses less computational time. Numerical examples are presented and the results are very satisfactory.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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