Stability of Finite Difference Schemes for Complex Diffusion Processes | Zendy

Adérito Araújo | Zendy; Sílvia Barbeiro | Zendy; Pedro Serranho | Zendy

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Stability of Finite Difference Schemes for Complex Diffusion Processes

Author(s) -

Adérito Araújo,

Sílvia Barbeiro,

Pedro Serranho

Publication year - 2012

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/110825789

Subject(s) - mathematics , context (archaeology) , nonlinear system , stability (learning theory) , finite difference , diffusion , finite difference method , image denoising , noise reduction , class (philosophy) , diffusion equation , mathematical analysis , algorithm , computer science , artificial intelligence , paleontology , physics , economy , quantum mechanics , machine learning , economics , biology , service (business) , thermodynamics

In this paper we present a rigorous proof for the stability of a class of finite difference schemes applied to nonlinear complex diffusion equations. Complex diffusion is a common and broadly used denoising procedure in image processing. To illustrate the theoretical results we present some numerical examples based on an explicit scheme applied to a nonlinear equation in the context of image denoising. (A correction is attached.)

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