Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  analyze the discrete maximum principle for the Beltrami color flow. The Beltrami flow can display linear as ll as nonlinear behavior according to the values of a parameter β, which represents the ratio beten spatial and color distances. In general, the standard schemes fail to satisfy the discrete maximum principle. In this work  show that a nonnegative second order difference scheme can be built for this flow only for small β, i.e. linear-like diffusion. Since this limitation is too severe,  construct a novel finite difference scheme, which is not nonnegative and satisfies the discrete maximum principle for all values of β. Numerical results support the analysis.
['Lorina Dascal', 'Adi Ditkowski', 'Nir A. Sochen']
I am writing a research paper on a idea On the Discrete Maximum Principle for the Beltrami Color Flow
[{"from": "human", "value": "I am writing a research paper on a idea On the Discrete Maximum Principle for the Beltrami Color Flow"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  analyze the discrete maximum principle for the Beltrami color flow. The Beltrami flow can display linear as ll as nonlinear behavior according to the values of a parameter \u03b2, which represents the ratio beten spatial and color distances. In general, the standard schemes fail to satisfy the discrete maximum principle. In this work  show that a nonnegative second order difference scheme can be built for this flow only for small \u03b2, i.e. linear-like diffusion. Since this limitation is too severe,  construct a novel finite difference scheme, which is not nonnegative and satisfies the discrete maximum principle for all values of \u03b2. Numerical results support the analysis."}]