Journal of Nepal Mathematical Society, Feb 26, 2024
In this paper, we study error estimates in the maximum norm in the context of solving Poisson's e... more In this paper, we study error estimates in the maximum norm in the context of solving Poisson's equation numerically when approximated the Five-Point Laplacian method using the discrete maximum principle. The primary objective is to assess the accuracy of this numerical approach in solving Poisson's equation and to provide insights into the behavior of error estimates. We focus on the estimates of maximum norm of the discrete functions defined on a grid in a unit square as well as in a square of side s, and estimate errors measured in the maximum norm.
In this paper, the two-dimensional electrostatic potential distribution problem has been solved n... more In this paper, the two-dimensional electrostatic potential distribution problem has been solved numerically using the finite difference approach using P oisson s equation in polar coordinates with Dirichlet s boundary condition inside a unit circular disc. We also use Gauss elimination method to solve numbers of linear equations to obtain solutions of unknowns at each grid point. The numerical solution to the same problem is contrasted with the analytic solution. Finally, we examine the absolute errors throughout a range of iterations to evaluate the accuracy of the schemes.
Journal of Nepal Mathematical Society, Feb 26, 2024
In this paper, we study error estimates in the maximum norm in the context of solving Poisson's e... more In this paper, we study error estimates in the maximum norm in the context of solving Poisson's equation numerically when approximated the Five-Point Laplacian method using the discrete maximum principle. The primary objective is to assess the accuracy of this numerical approach in solving Poisson's equation and to provide insights into the behavior of error estimates. We focus on the estimates of maximum norm of the discrete functions defined on a grid in a unit square as well as in a square of side s, and estimate errors measured in the maximum norm.
In this paper, the two-dimensional electrostatic potential distribution problem has been solved n... more In this paper, the two-dimensional electrostatic potential distribution problem has been solved numerically using the finite difference approach using P oisson s equation in polar coordinates with Dirichlet s boundary condition inside a unit circular disc. We also use Gauss elimination method to solve numbers of linear equations to obtain solutions of unknowns at each grid point. The numerical solution to the same problem is contrasted with the analytic solution. Finally, we examine the absolute errors throughout a range of iterations to evaluate the accuracy of the schemes.
Uploads
Papers by GBB Basnet