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Compact ADI method for solving parabolic differential equations. (English) Zbl 1004.65086
Summary: The authors first give a new alternating direction implicit (ADI) method for solving two-dimensionl parabolic differential equations. The idea of this method is using the fourth-order compact finite difference to discretize the second-order derivatives with respect to space, and using the Peaceman-Rachford ADI method to discretize the derivate with respect to time. Secondly, they prove the new ADI scheme is unconditionally stable with respect to the initial condition. Finally, they generalize the method to the three-dimensional case.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
65F10 Iterative numerical methods for linear systems
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