Cubic spline approximation based on half-step discretization for 2D quasilinear elliptic equations

Abstract

We report a new cubic spline approximation based on half-step discretization of order 2 in y- and order 4 in x-directions, for 2D quasi-linear elliptic PDEs. We use only two extra half-step points in x-direction and a central point. The cubic spline method is directly obtained from the continuity of first derivative terms and is applicable to elliptic problems irrespective of coordinates, which is the main advantage of our work. The error analysis of a model problem is discussed in details. Some benchmark problems are solved in order to test the numerical stability and accuracy of the method.

Keywords:

• Half-step discretization
• quasilinear elliptic PDEs
• polynomial cubic spline approximations
• cylindrical Poisson’s equation
• convection-diffusion PDE
• viscous Burgers’ equation
• high Reynolds number

Mathematics Subject Classifications (2010):

• 65N06

Acknowledgments

The authors thank the reviewers for their valuable suggestions, which substantially improved the standard of the paper.

Disclosure statement

The authors declare that they have no competing interests. All authors drafted the manuscript, and they read and approved the final version.

Additional information

Funding

This research work is supported by Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India, Sanction Order No.: CRG/2018/004608.