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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 7
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Research Article

High accuracy B-spline quasi-interpolants and applications in numerical analysis

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Pages 2035-2054 | Received 20 Jun 2021, Accepted 01 Dec 2021, Published online: 21 Dec 2021

References

  • de Boor C. A practical guide to splines. New York: Springer-Verlag; 1978.
  • Farin G. Curves and surfaces for CAGD. San Francisco: Morgan Kaufmann; 2002.
  • Buhmann M. Radial basis functions: theory and implementations. Cambridge: Cambridge University Press; 2003.
  • Powell M. Univariate multiquadric approximation: reproduction of linear polynomials. In Haussman W, Jetter K editors. Multivariate approximation and interpolation. Basel: Birkhäuser Verlag; 1990.
  • Beatson R, Powell M. Univariate multiquadric approximation: quasi-interpolation to scattered data. Constr Approx. 1992;8:275–288.
  • Wu Z, Schaback R. Shape preserving properties and convergence of univariate multiquadric quasi-interpolation. Acta Math Appl Sin. 1994;10:441–446.
  • Feng R, Zhou X. A kind of multiquadric quasi-interpolation operator satisfying any degree polynomial reproduction property to scattered data. J Comput Appl Math. 2011;235:1502–1514.
  • Waldron S. Increasing the polynomial reproduction of a quasi-interpolation operator. J Approx Theory. 2009;161:114–126.
  • Rabut C. Multivariate divided differences with simple knots. SIAM J Numer Anal. 2000;38:1294–1311.
  • Wu R, Wu T, Li H. A family of multivariate multiquadric quasi-interpolation operators with higher degree polynomial reproduction. J Comput Appl Math. 2015;274:88–108.
  • Ling L. A univariate quasi-multiquadric interpolation with better smoothness. Comput Math Appl. 2004;48:897–912.
  • Hon YC, Wu Z. A quasi-interpolation method for solving ordinary differential equations. Int J Numer Methods Eng. 2000;48:1187–1197.
  • Chen R, Wu Z. Solving partial differential equation by using multiquadric quasi-interpolation. Appl Math Comput. 2007;186:1502–1510.
  • Gao Q, Wu Z, Zhang S. Adaptive moving knots meshless method for simulating time dependent partial differential equations. Eng Anal Bound Elem. 2018;96:115–122.
  • Sablonnière P. Univariate spline quasi-interpolants and applications to numerical analysis. Rend Sem Mat Univ Pol Torino. 2005;63:211–222.
  • Dagnino C, Remogna S. Differentiation based on optimal local spline quasi-interpolants with applications. AIP Conf Proc. 2010;1281:2025–2028.
  • Remogna S. Pseudo-spectral derivative of quadratic quasi-interpolant splines. Rend Semin Mat Univ Politech Torino. 2009;67:351–362.
  • Mazzia F, Sestini A. Quadrature formulas descending from BS Hermite spline quasi-interpolation. J Comput Appl Math. 2012;236:4105–4118.
  • Calabro F, Falini A, Sampoli ML, et al. Efficient quadrature rules based on spline quasi-interpolation for application to IGA-BEMs. J Comput Appl Math. 2018;338:153–167.
  • Zhu C, Wang R. Numerical solution of Burgers' equation by cubic B-spline quasi-interpolation. Appl Math Comput. 2009;208:260–272.
  • Zhang J, Zheng J, Gao Q. Numerical solution of the Degasperis–Procesi equation by the cubic B-spline quasi-interpolation method. Appl Math Comput. 2018;324:218–227.
  • Kumar R, Choudhary A, Baskar S. Modified cubic B-spline quasi-interpolation numerical scheme for hyperbolic conservation laws. Appl Anal. 2020;99:158–179.
  • Han X. Multi-node higher order expansions of a function. J Approx Theory. 2003;124:44–88.

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