Two very specific cases for separate node ascending derivatives expansion (SNADE)

Bodur, Derya; Demіralp, Metin

doi:10.1063/1.4938941

Cited by 3 publications

(2 citation statements)

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“…Figure 4 has been constructed for the case x p = −2, in other words, for the function 1∕(x + 2); x 1 and x 2 nodal point values are chosen as 10 and 11, respectively, while x is taken equal to 5. Thus, the range of convergence of x appears to be [11,16] as can be seen from this figure.…”

Section: Numerical Implementationsmentioning

confidence: 67%

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Influence of a simple pole on the convergence of separate node ascending derivatives expansion (SNADE) on a sequence of nodes alternating between 2 values

Bodur

Demіralp

2018

Math Methods in App Sciences

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This work focuses on the influence of a simple pole on a new function representing method we called separate node ascending derivatives expansion (SNADE) convergence characteristics. Even though SNADE can be somehow considered as a new Taylor series expansion, it is distincted from Taylor series expansion by its different nodal points using features. This paper focuses on certain details of SNADE about convergence and its validity. Beyond that, this research focusing on the influence of a simple pole location in the function on the convergence characteristics involves completely new original findings and reported in this paper where a specific importance is given to the case where the SNADE nodal sequence is composed of elements alternating between two nodal values.

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Section: Numerical Implementationsmentioning

confidence: 67%

“…Separate node ascending derivatives expansion is based on the derivative integration formula. [11][12][13][14][15][16] The core topic of this work, SNADE, is also based on the same identity. However, it uses infinitely many expansion points in each step of its repeated utilization.…”

Section: Introductionmentioning

confidence: 99%