Numerical simulation of the coupled viscous Burgers equation using the Hermite formula and cubic B-spline basis functions | Zendy

Muhammad Abdullah | Zendy; Muhammad Yaseen | Zendy; Manuel De la Sen | Zendy

Open Access

Numerical simulation of the coupled viscous Burgers equation using the Hermite formula and cubic B-spline basis functions

Author(s) -

Muhammad Abdullah,

Muhammad Yaseen,

Manuel De la Sen

Publication year - 2020

Publication title -

physica scripta

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.415

H-Index - 83

eISSN - 1402-4896

pISSN - 0031-8949

DOI - 10.1088/1402-4896/abbf1f

Subject(s) - hermite polynomials , discretization , hermite spline , burgers' equation , monotone cubic interpolation , mathematics , mathematical analysis , cubic hermite spline , basis function , b spline , piecewise , hermite interpolation , dimension (graph theory) , stability (learning theory) , thin plate spline , spline interpolation , partial differential equation , pure mathematics , computer science , nearest neighbor interpolation , trilinear interpolation , machine learning , statistics , linear interpolation , polynomial , bilinear interpolation

A numerical procedure dependent on the cubic B-spline and the Hermite formula is developed for the coupled viscous Burgers’ equation (CVBE). The method uses a combination of the Hermite formula and the cubic B-spline for discretization of the space dimension while the time dimension is approximated using the typical finite differences. A piecewise continuous sufficiently smooth function is obtained as a solution which allows to approximate solution at any location in the domain of interest. The scheme is tested for stability analysis and is proved to be unconditionally stable. Numerical experiments and comparison of outcomes reveal that the suggested scheme comes up with better accuracy and is extremely productive.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research