Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Comparative Study of Crank-Nicolson and Modified Crank-Nicolson Numerical methods to solve linear Partial Differential Equations
View through CrossRef
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
Indian Society for Education and Environment
Title: Comparative Study of Crank-Nicolson and Modified Crank-Nicolson Numerical methods to solve linear Partial Differential Equations
Description:
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.
Related Results
Primerjalna književnost na prelomu tisočletja
Primerjalna književnost na prelomu tisočletja
In a comprehensive and at times critical manner, this volume seeks to shed light on the development of events in Western (i.e., European and North American) comparative literature ...
Numerical Solution of Burgers' Equation Using Discrete Symmetries
Numerical Solution of Burgers' Equation Using Discrete Symmetries
Crank-Nicolson method is a finite difference scheme used to solve the
heat and other parabolic partial differential equations. In order to
solve the Burgers’ equation which is para...
Exploring Large Language Models Integration in the Histopathologic Diagnosis of Skin Diseases: A Comparative Study
Exploring Large Language Models Integration in the Histopathologic Diagnosis of Skin Diseases: A Comparative Study
Abstract
Introduction
The exact manner in which large language models (LLMs) will be integrated into pathology is not yet fully comprehended. This study examines the accuracy, bene...
An operative approach to solve Homogeneous differential--anti-differential equations
An operative approach to solve Homogeneous differential--anti-differential equations
In this work, we extend the theory of differential equations through a
new way. To do this, we give an idea of differential–anti-differential
equations and dene ordinary as well as...
Research On Roundness Error Consistency Model For Crank Journal Cylindrical grinding
Research On Roundness Error Consistency Model For Crank Journal Cylindrical grinding
Abstract
Cylindrical grinding is an important way to form the external shape error of the crank journal, and the accuracy consistency directly affects the interchangeabilit...
Soham Transform in Fractional Differential Equations
Soham Transform in Fractional Differential Equations
Objectives: Soham transforms is one of the appropriate tools for solving fractional differential equations that are flexible enough to adapt to different purposes. Methods: Integra...
Research on a Class of First-Order Nonlinear Nonhomogeneous Variable Coefficient Ordinary Differential Equations Based on Elastic Transformation
Research on a Class of First-Order Nonlinear Nonhomogeneous Variable Coefficient Ordinary Differential Equations Based on Elastic Transformation
This paper mainly studies the problem of solving a class of first-order
nonlinear non-homogeneous ordinary differential equations with variable
coefficients， which can be transform...
Pioneering Numerical Techniques for Solving Differential Equations - A Comprehensive overview
Pioneering Numerical Techniques for Solving Differential Equations - A Comprehensive overview
The field of numerical analysis studies the application of mathematics to solve problems of practical importance. When solving differential equations derived from real-world scenar...