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在基本计算系统中实现切比雪夫多项式的算法 被引量:2

Computing Chebyshev Polynomials in a Basic Computing System
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摘要 提出了一个仅使用基本运算加、减和移位计算切比雪夫多项式的坐标旋转算法,证明了收敛性,讨论了误差估计.算法编码占用空间很小,适合在微计算系统中使用. In this paper,a coordinates rotating algorithm for computing Chebyshev polynomials with only basic operations adding,subtracting,and shifting was put forward.Convergence of the algorithm was proved and error estimation of the algorithm was discussed.
作者 谷峰
出处 《数学的实践与认识》 CSCD 北大核心 2010年第20期83-88,共6页 Mathematics in Practice and Theory
关键词 坐标旋转算法 切比雪夫多项式 基本计算系统 coordinates rotating algorithm chebyshev polynomial basic computing system
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参考文献4

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共引文献14

同被引文献15

  • 1Cui M G, Chen C. The exact solution of nonlinear age-structured population model[J]. Nonlinear Anal: Real World Appl, 2007, 8: 1096-1112.
  • 2Liu W, Zhang Q. Convergence of numerical solutions to stochastic age-structured system of three species[J]. Applied Mathematics and Computation, 2011 218: 3973-3980.
  • 3Krzyianowski P, Wrzosek D, Wit D. Discontinuous Galerkin method for piecewise regular solution to the nonlinear age-structured population model[J]. Mathematical Biosciences, 2006, 203: 277-300.
  • 4Pang W K, Li R, Liu M, Convergence of the semi-implicit Euler method for stochastic age-dependent population equations[J]. Applied Mathematics and Computation, 2008, 195: 466-474.
  • 5Yousefi S A, Behroozifar M, Dehghan M. Numerical solution of the nonlinear age-structured popu- lation models by using the operational matrices of Bernstein polynomials[J]. Applied Mathematical Modeling, 2012, 36: 945-963.
  • 6Elbarbary E M E, Chebyshev finite difference method for the solution of boundary-layer equations[J]. Appl Math Comput, 2005, 160: 487-498.
  • 7Heydari M H, Hooshmandasl M R, Maalek F M. Ghaini, A new approach of the Chebyshev wavelets method for partial differential equations with boundary conditions of the telegraph type[J]. Applied Mathematical Modeling, 2014, 38: 1597-1606.
  • 8Doha E H, Abd-Elhameed W M, Bassuony M A, New algorithms for solving high even-differential equations using third and fourth Chebyshev-Galerkin method[J]. J Comput Phys, 2013, 236: 563- 579.
  • 9Gh S, Hosseini F. Mohammadi A new operational matrix of derivative for Chebyshev wavelets and its applications in solving ordinary differential equations with non analytic solution[J]. Appl Math Sci, 2011, 5(51): 2537-2548.
  • 10Tavassoli Kajani M, Hadi Vencheh A, Ghasemi M. The Chebyshev wavelets operational matrix of integration and product operation matrix[J]. Int J Comput Math, 2009, 86(7): 1118-1125.

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