Higher-Order Difference and Higher-Order Splitting Methods for 2D Parabolic Problems with Mixed Derivatives
نویسندگان
چکیده
In this article we discuss a combination between fourth-order finite difference methods and fourth-order splitting methods for 2D parabolic problems with mixed derivatives. The finite difference methods are based on higher-order spatial discretization methods, whereas the timediscretization methods are higher-order discretizations using CrankNicolson or BDF methods. The splitting methods are higher-order compact alternating direction implicit (ADI) methods. Here we construct a fourth-order splitting method with respect to the weighting factors. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Mathematics Subject Classifications: 35J60, 35J65, 65M99, 65N12, 65Z05, 74S10, 76R50, 80A20, 80M25
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