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

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.

Keywords

• b spline|spline quasi-intepolation|saint-venant equation|numerical solutions of partial differential equations