Mimetic finite difference methods for restoration of fundus images for automatic detection of glaucoma suspects

Villamizar, Jorge; Calderón, Giovanni; Carrillo, Julio; Rozo, Lola Xiomara Bautista; Carrillo, Juan; Rueda, J. A.; Castillo, José E.

doi:10.1080/21681163.2021.1914733

Cited by 5 publications

(3 citation statements)

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“…In recent years, several applications of a similar, not equal, implicit mimetic scheme for the heat equation based on the mimetic operators described in this paper have been published in academic journals [17] [18]. In our notation, the implicit mimetic scheme proposed in those articles, in its simplest form, takes the expression ( )…”

Section: Discussionmentioning

confidence: 99%

“…This appendix presents the finite difference equations associated to the implicit mimetic scheme in the case of a general transient diffusion equation (17). Following the style of the paper the equations associated to the first inner node, the second inner node, and the generic inner node will be presented.…”

Section: Appendixmentioning

confidence: 99%

“…Matrix K has order n + 1 and it contains the projections of k at the block edges. Description of the equations generated by (17) will be presented in Appendix. They won't be used in the sequel.…”

mentioning

confidence: 99%

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A New Analysis of an Implicit Mimetic Scheme for the Heat Equation

Nava¹,

Guevara-Jordan²

2023

JAMP

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A mimetic finite difference scheme for the transient heat equation under Robin's conditions is presented. The scheme uses second order gradient and divergence mimetic operators, on a staggered grid, to approximate the space derivatives. The temporal derivative is replaced by a first order backward difference approximation to obtain an implicit formulation. The resulting scheme contains nonstandard finite difference stencils. An original convergence analysis by the matrix's method shows that the proposed scheme is unconditionally stable. A comparative study against standard finite difference schemes, based on central difference or first order one side approximations, reveals the advantages of our scheme without being its implementation more expensive or difficult to achieve.

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Section: Discussionmentioning

confidence: 99%

Section: Appendixmentioning

confidence: 99%