An efficient scheme for solution of two-dimensional Laplace's equation

Ariba Arshad; R.C. Mittal; Seema Sharma

An efficient scheme for solution of two-dimensional Laplace's equation

Authors

Ariba Arshad

Department of Mathematics and Statistics, Gurukula Kangri Vishwavidyalaya, Haridwar, Uttarakhand

R.C. Mittal

Department of Mathematics, Jaypee Institute of Technology, Noida, Uttar Pradesh

Seema Sharma

Department of Mathematics and Statistics, Gurukula Kangri Vishwavidyalaya, Haridwar, Uttarakhand

DOI: https://doi.org/10.21467/proceedings.100.3

Synopsis

The main objective of this paper is to analyse the solution of two-dimensional Laplace's equation using an efficient scheme, which is based on collocation of modied bi-cubic Bspline functions. This scheme is applied to obtain the approximate solution of Laplace's equation with Dirichlet boundary conditions for two illustrative examples. For these examples, the results obtained by this scheme have been compared with exact solutions and solutions available in literature to check the accuracy and versatility of present scheme.