17,698 research outputs found
On the Construction of Splitting Methods by Stabilizing Corrections with Runge-Kutta Pairs
In this technical note a general procedure is described to construct
internally consistent splitting methods for the numerical solution of
differential equations, starting from matching pairs of explicit and diagonally
implicit Runge-Kutta methods. The procedure will be applied to suitable
second-order pairs, and we will consider methods with or without a mass
conserving finishing stage. For these splitting methods, the linear stability
properties are studied and numerical test results are presented.Comment: 18 page
ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation
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