Comparative Study of Crank-Nicolson and Modified Crank-Nicolson Numerical methods to solve linear Partial Differential Equations

Tejaskumar C Sharma; Shreekant P Pathak; Gargi Trivedi

doi:10.17485/IJST/v17i10.1776

Article

Comparative Study of Crank-Nicolson and Modified Crank-Nicolson Numerical methods to solve linear Partial Differential Equations

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i10.1776

Year: 2024, Volume: 17, Issue: 10, Pages: 924-931

Original Article

Comparative Study of Crank-Nicolson and Modified Crank-Nicolson Numerical methods to solve linear Partial Differential Equations

Tejaskumar C Sharma^1*, Shreekant P Pathak², Gargi Trivedi³

¹Research Scholar, Department of Mathematics, N V Patel College of Pure & Applied Sciences, The Charutar Vidyamandal University, Vallabh Vidyanagar, Anand, Gujarat, India
²Assistant Professor, Department of Mathematics, N V Patel College of Pure & Applied Sciences, The Charutar Vidyamandal University, Vallabh Vidyanagar, Anand, Gujarat, India
³Department of Applied Mathematics, Faculty of Technology and Engineering, The Maharaja Sayajirao University of Baroda, Vadodara, Gujarat, India

*Corresponding Author
Email: [email protected]

Received Date:17 July 2023, Accepted Date:30 January 2024, Published Date:27 February 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: This paper aims to address the limitations of the Crank-Nicolson Finite Difference method and propose an improved version called the modified Crank-Nicolson method. Methods: Utilized implicit discretization in time and space, with parameters k = 0.001, h = 0.1, and γ = 0.1. Conducted extensive testing on various partial differential equations. Findings: Results, displayed in Table 1, showcase the method's stability and accuracy. Comparative analysis in Table 2 demonstrates the Modified Crank-Nicolson method consistently outperforming the traditional approach, reaffirming its superiority in accuracy. Novelty: The modified Crank-Nicolson method offers a significant enhancement to the traditional Crank-Nicolson finite difference method, making it a valuable tool for effectively solving partial differential equations.

Keywords: CrankNicolson Method, Modified CrankNicolson Method, Finite Difference, Partial Differential Equations, Parabolic Equations, Python Software

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Copyright

© 2024 Sharma et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)