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- W4375947247 abstract "In a recent contribution the Discrete Taylor Transform and Inverse Transform (D-TTIT) in one dimension was introduced, [1]. Based on a simple Toy Model, the current work extends the originally conceived D-TTIT to 2D. By analogy, the D-TTIT algorithm naturally extends from 2D to 3D. The presentation is based on a 2D discrete lattice, along with properly-chosen monomial products, <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$x^{m}y^{n}(m,nin mathbb{N})$</tex> , as initial continuous basis functions. The monomial products, sampled at the lattice points, generate a discrete basis <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$vertmathcal{B}^{m,n} >$</tex> . The main result in this work is the discovery that the dual basis associated with <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$vertmathcal{B}^{m,n} >$</tex> corresponds to the desired discrete mixed derivative operators <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>$vert mathcal{D}^{m,n} >$</tex> . The constructed basis and dual basis satisfy the mutual orthogonality properly, and the resolution of the identity operator. Future work will examine the validity of these findings in curvilinear and logically rectangular coordinates." @default.
- W4375947247 created "2023-05-10" @default.
- W4375947247 creator A5083115376 @default.
- W4375947247 date "2023-03-26" @default.
- W4375947247 modified "2023-09-29" @default.
- W4375947247 title "Discrete Taylor Transform and Inverse Transform in 2D and 3D" @default.
- W4375947247 doi "https://doi.org/10.23919/aces57841.2023.10114785" @default.
- W4375947247 hasPublicationYear "2023" @default.
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