解决线性偏微分方程的 Crank-Nicolson 和修正 Crank-Nicolson 数值方法比较研究

Indian journal of science and technology Pub Date : 2024-03-01 DOI:10.17485/ijst/v17i10.1776

Tejaskumar Sharma, Shreekant Pathak, Gargi J Trivedi

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引用次数: 0

摘要

目的：本文旨在解决 Crank-Nicolson 有限差分法的局限性，并提出一种改进版的 Crank-Nicolson 方法。方法：利用时间和空间的隐式离散，参数 k = 0.001，h = 0.1，γ = 0.1。对各种偏微分方程进行了广泛的测试。结果表 1 中的结果显示了该方法的稳定性和准确性。表 2 中的对比分析表明，改进型 Crank-Nicolson 方法的性能始终优于传统方法，再次证明了其在准确性方面的优势。新颖性：改进的 Crank-Nicolson 方法显著提高了传统 Crank-Nicolson 有限差分法的性能，使其成为有效求解偏微分方程的重要工具。关键词Crank-Nicolson方法修正Crank-Nicolson方法有限差分偏微分方程抛物线方程 Python软件

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

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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Indian journal of science and technology

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