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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 Crank-Nicolson or BDF methods. The splitting methods are higher-order compact alternating direction implicit (ADI) methods. Here we construct a fourth-orderdoi:10.12988/imf.2007.07308 fatcat:yvjmzh3nojevtoti4zi5bbm2cu