Computer Science

Computer Science ›› 2023, Vol. 50 ›› Issue (4): 125-132.doi: 10.11896/jsjkx.220800118

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Numerical Solution of Saint-Venant Equation by Cubic B-spline Quasi-interpolation

QIAN Jiang, ZHANG Ding   

  1. College of Science,Hohai University,Nanjing 211100,China
  • Received:2022-08-12 Revised:2022-11-09 Online:2023-04-15 Published:2023-04-06
  • About author:QIAN Jiang,born in 1981,Ph.D,asso-ciate professor,master supervisor.His main research interests include numerical approximation,computational geometry,multivariate spline,finite element,etc.
    ZHANG Ding,born in 1999,postgra-duate.His main research interests include numerical approximation and computational geometry.

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Abstract: Firstly,the error estimates of cubic spline quasi-intepolating operators are derived for continuous differential function with different orders.Secondly,cubic B-spline quasi-interpolation is used to get the numerical solution of Saint-Venant equation.Specifically,the derivatives of the quasi-interpolation are used to approximate the spatial derivative of the dependent variable and forward difference method is used to approximate the time derivative of the dependent variable.Finally,the numerical solutions are compared with the solution obtained by the fourth order Runge-Kutta method and the leapfrog scheme.Then numerical examples show that cubic spline quasi-intepolating method has some advantages.

Key words: B spline, Spline quasi-intepolation, Saint-Venant equation, Numerical solutions of partial differential equations

CLC Number: 

  • O241.82
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