|
|||||
|
|
Cubic spline approximation based on half-step discretization for 2D quasilinear elliptic equations |
|
| Authors: | R K Mohanty Ravindra Kumar Nikita Setia |
| Affiliation: | 1. Department of Mathematics, South Asian University, New Delhi, India rmohanty@sau.ac.in![ORCID Icon]({"type":"image","src":"/templates/jsp/images/orcid.png"} "ORCID Icon") https://orcid.org/0000-0001-6832-1239;3. Department of Mathematics, Rajdhani College, University of Delhi, New Delhi, India https://orcid.org/0000-0001-8441-2966;4. Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, New Delhi, India https://orcid.org/0000-0002-5337-3367 |
| Abstract: | 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 |