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

Tejaskumar C Sharma,Research Scholar, Department Of Mathematics, N V Patel College Of Pure & Applied Sciences, The Charutar Vidyamandal University, Vallabh Vidyanagar, Anand, Gujarat, India ,Shreekant P Pathak,Gargi Trivedi

doi:10.17485/ijst/v17i10.1776

Tejaskumar C Sharma, Research Scholar, Department Of Mathematics, N V Patel College Of Pure & Applied Sciences, The Charutar Vidyamandal University, Vallabh Vidyanagar, Anand, Gujarat, India

Open Access

https://doi.org/10.17485/ijst/v17i10.1776

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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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