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Evaluation Methods of Spline

  • Dhananjay Singh
  • Madhusudan Singh
  • Zaynidinov Hakimjon
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

This paper outlines the methods of spline and outlines the best tools and their features for signal processing and analysis. An extensive analysis of existing hardware intended for digital processing indicated that architecture and availability of hardware implemented special multiplication special multiplication commands, parallel accumulative multiplication at Harvard could allow wide use of modern digital signal processors for implementation of spline-recovery methods. MATLAB instrumental tools help in accelerating the application development process due to tools like language for working with matrixes, visual modelling and automatic generation of the software code, and various other packages that offer different knowledge inputs in a single environment. MATLAB’s powerful and easy-to-use language for matrix computations provides a natural representation for signals; thus, it is highly applicable in digital processing of signals. Additional packages of applied MATLAB (toolboxes) and Simulink blocks are the richest sources of premade functions for further extension, basic blocks for construction of models and visual tools visually working with signals.

References

  1. 1.
    Y.-M. Wnag, L. Ren, G. Ao, Z. Sun, H. Zhang, A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications. J. Comput. Phys. 259, 33–50 (2014)MathSciNetCrossRefGoogle Scholar
  2. 2.
    A.A. Alikhanov, A new difference scheme for the time fractional diffusion equation. J. Comput. Phys. 280, 424–438 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    H. Zhang, X. Yang, D. Xu, A high-order numerical method for solving the 2D fourth order reaction-diffusion equation. Numer. Algorithms 1–29 (2018)Google Scholar
  4. 4.
    C.P. Li, R.F. Wu, H.F. Ding, High-order approximation to Caputo derivative and Caputo-type advection-diffusion equations. Commun. Appl. Ind. Math. 6(2), e-536 (2014)Google Scholar
  5. 5.
    H. Li, J. Cao, C. Li, High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (III). J. Comput. Appl. Math. 299, 159–175 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    C. Lv, C. Xu, Error analysis of a high order method for time-fractional diffusion equations. SIAM J. Sci. Comput. 38, A2699–A2724 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Z.Q. Li, Y.B. Yan, N.J. Ford, Error estimates of a high order numerical method for solving linear fractional differential equations. Appl. Numer. Math. 114, 201–220 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Y.B. Yan, K. Pal, N.J. Ford, Higher order numerical methods for solving fractional differential equations. BIT Numer. Math. 54, 555–584 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    M. Dehghan, M. Abbaszadeh, Two meshless procedures: moving Kriging interpolation and element-free Galerkin for fractional PDEs. Appl. Anal. 96, 936–969 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Dehghan, M. Abbaszadeh, Element free Galerkin approach based on the reproducing kernel particle method for solving 2D fractional Tricomi-type equation with Robin boundary condition. Comput. Math. Appl. 73, 1270–1285 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    X. Yang, H. Zhang, D. Xu, J. Sci. Comput. (2018).  https://doi.org/10.1007/s10915-018-0672-3MathSciNetCrossRefGoogle Scholar
  12. 12.
    B. Jin, R. Lazarov, J. Pasciak, Z. Zhou, Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion. IMA J. Numer. Anal. 35, 561–582 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    B. Jin, R. Lazarov, Y. Liu, Z. Zhou, The Galerkin finite element method for a multi-term time-fractional diffusion equation. J. Comput. Phys. 281, 825–843 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    W. McLean, K. Mustapha, Time-stepping error bounds for fractional diffusion problems with non-smooth initial data. J. Comput. Phys. 293, 201–217 (2015)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Z. Wang, S. Vong, Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation. J. Comput. Phys. 277, 1–15 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Dhananjay Singh
    • 1
  • Madhusudan Singh
    • 2
  • Zaynidinov Hakimjon
    • 3
  1. 1.Department of Electronics EngineeringHankuk University of Foreign Studies (Global Campus)YonginKorea (Republic of)
  2. 2.School of Technology Studies, Endicott College of International StudiesWoosong UniversityDaejeonKorea (Republic of)
  3. 3.Head of Department of Information TechnologiesTashkent University of Information TechnologiesTashkentUzbekistan

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