High accuracy cubic spline approximation for two dimensional quasi-linear elliptic boundary value problems |
| |
Authors: | RK Mohanty MK Jain Deepika Dhall |
| |
Institution: | 1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India;2. Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India |
| |
Abstract: | We report a new 9 point compact discretization of order two in y- and order four in x-directions, based on cubic spline approximation, for the solution of two dimensional quasi-linear elliptic partial differential equations. We describe the complete derivation procedure of the method in details and also discuss how our discretization is able to handle Poisson’s equation in polar coordinates. The convergence analysis of the proposed cubic spline approximation for the nonlinear elliptic equation is discussed in details and we have shown under appropriate conditions the proposed method converges. Some physical examples and their numerical results are provided to justify the advantages of the proposed method. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|