Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method Article Swipe

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Md. Roknujjaman , Mohammad Asif Arefin , Atish Kumar Joarder ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.28919/cpr-pajm/3-24

The method of lines (MOL) is a solution procedure for solving partial differential equation (PDE) and the Crank-Nicholson method (CNM) is an implicit finite difference method, used to solve the elliptic equation and similar partial differential equations numerically. In this study, the numerical techniques were introduced to solve elliptic partial differential equation (PDE) together with initial and boundary conditions. The Poisson equation was considered as an elliptic PDE. Particularly, two methods were used to solve a two-dimensional Poisson equation numerically, such as the method of lines (MOL) and Crank-Nicholson method (CNM). The implementation of the solutions was done using Microsoft office spreadsheet and MATLAB programing language. Lastly, the numerical solutions were presented graphically which was obtained with method of lines along with Crank-Nicholson method.

Related Topics

Crank (Mechanism)

Partial Differential Equation

Mathematics

Mathematical Analysis

Differential Equation

Numerical Analysis

Geometry

Concepts

Crank Elliptic partial differential equation Partial differential equation Mathematics Method of lines Elliptic curve First-order partial differential equation Crank–Nicolson method Mathematical analysis Differential equation Applied mathematics Numerical analysis Geometry Ordinary differential equation Differential algebraic equation Cylinder

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Type: article
Language: en
Landing Page: https://doi.org/10.28919/cpr-pajm/3-24
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DOI: https://doi.org/10.28919/cpr-pajm/3-24

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Title: Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method

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Publication year: 2024

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Publication date: 2024-12-23

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Authors: Md. Roknujjaman, Mohammad Asif Arefin, Atish Kumar Joarder

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Landing page: https://doi.org/10.28919/cpr-pajm/3-24

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Concepts: Crank, Elliptic partial differential equation, Partial differential equation, Mathematics, Method of lines, Elliptic curve, First-order partial differential equation, Crank–Nicolson method, Mathematical analysis, Differential equation, Applied mathematics, Numerical analysis, Geometry, Ordinary differential equation, Differential algebraic equation, Cylinder

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