Author(s):
1. Rabnawaz Mallah:
Sukkur IBA University, Pakistan; Shah Abdul Latif University, Khairpur, Pakistan
2. Wajid Ahmed Siyal:
Sukkur IBA University, Pakistan
3. Saira Aslam:
University Malaysia Sarawak
4. Muhammad Suleman Sial:
Department of Basic Sciences and Related Studies,Mehran University of Engineering and Technology, Pakistan
5. Inayatullah Soomro:
Shah Abdul Latif University, Khairpur, Pakistan
Abstract:
Numerous techniques exist for solving and describing the Partial differential equation’s mathematical and computational model. The Laplacian operator is one of the most effective techniques for solving linear and nonlinear partial differential equations. It is quick, and researchers use it frequently because of its modern technique and high accuracy in results. The Crank-Nicolson (CN) scheme in the Cartesian coordinate system has been discussed in this research work. Using this method, a numerical approximation scheme in Cartesian coordinate system has been discretized on a 5 point stencil, extendable to nine points. The Tailor Series was used to discretize this scheme on 5-point stencils, which will be used in FORTRAN code for numerical approximation and can be visualized in OPEDX software. The Nicolson scheme is a finite difference scheme used to solve partial differential equations such as heat, wave, and diffusion equations in both 1-D and 2-D. Because of his extendable stencil, it will create accuracy and stability in the novel results of the scheme. These extendable stencils will reduce the error of the scheme and will assist researchers in finding novel results by solving ODES and PDES using the CN method.
Page(s):
13-20
DOI:
DOI not available
Published:
Journal: VFAST Transactions on Mathematics, Volume: 10, Issue: 2, Year: 2022
Keywords:
CrankNicolsons method
,
35L05
,
Laplacian
,
35J10
,
Polar coordinate system Subject Classification 35J05
,
35K05
,
Finite differences method
References:
References are not available for this document.
Citations
Citations are not available for this document.