Construction of New Fractal Interpolation Functions Through Integration Method

Agathiyan, A.; Gowrisankar, A.; Priyanka, T. M. C.

doi:10.1007/s00025-022-01666-9

Cited by 18 publications

(3 citation statements)

References 20 publications

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“…Since the fractal functions are developed using the theory of iterated function system, the iteration process generates more number of points thus using fractal functions for reconstruction always increases the accuracy of any provided dynamical system. Various interesting results on the fractal interpolation functions and its types have been presented by many researchers, see for instance [42][43][44]. Owing to the complex and self-similar nature of the perturbed dynamical system, fractal interpolation functions are used to reconstruct the system besides its dynamical features are explored.…”

Section: Introductionmentioning

confidence: 99%

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

et al. 2023

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Propagation of small-amplitude ion-acoustic waves and its fractal representations is investigated in an electron-ion quantum plasma with separated spin electrons in the framework of the KdV and EKdV equations derived using reductive perturbation technique. The two evolution equations are transformed into planar dynamical systems by using suitable traveling wave transformation. Qualitatively diﬀerent phase portraits of these two systems are drawn with their respective Sagdeev’s pseudopotential curves and surface plots. Distinct orbits in the phase portraits give rise to distinct wave solutions. Periodic and superperiodic wave solutions are investigated numerically and solitary wave solutions are derived analytically. The eﬀect of parameters such as Mach number, direction cosine, spin polarization and frequency ratio on these wave solutions are presented. For instance, it is seen that the spin density polarization ratio has an impressive eﬀect on the amplitude of the wave solution, while the frequency ratio has no eﬀect on its amplitude. Also, we have provided a physical explanation for our ﬁnding. Further, the dynamical features of the original system and reconstructed system using fractal interpolation function are investigated under the external forcing term. Chaotic and quasiperiodic phenomena are observed for diﬀerent initial conditions. The results may help to better understand the degenerate electron gas that exists in astrophysical bodies and laboratory plasmas such as paramagnetic and ferromagnetic metals in exposing the external magnetic ﬁeld.

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Section: Introductionmentioning

confidence: 99%

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

et al. 2023

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“…The classical integral of a linear fractal interpolation function is investigated in [ 1 ]. It is trivial that the integration of a function is associated with the area under the graph of the function.…”

Section: Introductionmentioning

confidence: 99%

Numerical integration of bivariate fractal interpolation functions on rectangular domains

Aparna

Paramanathan

2023

Eur. Phys. J. Spec. Top.

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This paper primarily focuses on the derivation of fractal numerical integration for the data sets corresponding to two variable signals defined over a rectangular region. Evaluating numerical integration results through the fractal method helps achieve accurate results with minimum computation effort. The formulation of the fractal numerical integration is achieved by considering the recursive relation satisfied by the bivariate fractal interpolation functions for the given data set. The points in the data set have been used to evaluate the coefficients of the iterated function systems. The derivation of these coefficients considering the index of the subrectangles, and the integration formula has been proposed using these coefficients. The bivariate fractal interpolation functions constructed using these coefficients are then correlated with the bilinear interpolation functions. Also, this paper derives a formula for the freely chosen vertical scaling factor that has been used in reducing the approximation error. The obtained formula of the vertical scaling factor is then used in establishing the convergence of the proposed method of integration to the traditional double integration technique through a collection of lemmas and theorems. Finally, the paper concludes with an illustration of the proposed method of integration and the analysis of the numerical integral results obtained for the data sets corresponding to four benchmark functions.

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“…In this way, the field of Approximation Theory has been considerably enriched with different models. The contributions in the area of fractal interpolation are recent and numerous, both in theory as well as in applications (see, for instance, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]).…”

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confidence: 99%

Fractal Curves on Banach Algebras

Navascués

2022

Fractal Fract

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Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as Banach spaces and algebras, with minimal conditions and structures, transcending in this way the numerical underlying scenario. This is performed via fixed point of an operator defined on a b-metric space of Banach-valued functions with domain on a real interval. The sets of images may provide uniparametric fractal collections of measures, operators or matrices, for instance. The defining operator is linked to a collection of maps (or iterated function system, and the conditions on these mappings determine the properties of the fractal function. In particular, it is possible to define continuous curves and fractal functions belonging to Bochner spaces of Banach-valued integrable functions. As residual result, we prove the existence of fractal functions coming from non-contractive operators as well. We provide new constructions of bases for Banach-valued maps, with a particular mention of spanning systems of functions valued on C*-algebras.

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Construction of New Fractal Interpolation Functions Through Integration Method

Cited by 18 publications

References 20 publications

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

Propagation of ion-acoustic wave and its fractal representations in spin polarized electron plasma

Numerical integration of bivariate fractal interpolation functions on rectangular domains

Fractal Curves on Banach Algebras

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