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Research Paper | Mathematics | India | Volume 12 Issue 4, April 2023 | Popularity: 5.2 / 10

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Numerical Solution of the 2 - Dimensional Heat Equation using Python: Implementation and Analysis

Dr. Vivek Parkash

Abstract: Python is widely acknowledged for its formidable ability in handling intricate mathematical challenges, including the simulation of the two - dimensional heat equation-a critical partial differential equation governing temperature distribution evolution in a specified region over varying time steps. The versatility of Python, coupled with its extensive library support, positions it as a premier choice for conducting numerical simulations and analyses. This encompasses solving the heat equation through diverse methods such as finite differences, finite elements, or spectral methods. This paper is focused on exploring the finite difference method as a tool to solve the two - dimensional heat equation. It investigates the temperature distribution within a predefined domain across a range of parameter configurations. The process involves discretizing the partial differential equation in both spatial dimensions (x, y) and progressing in time steps t using an iterative approach.

Keywords: python, mathematics, finite difference, heat equation, temperature distribution

Edition: Volume 12 Issue 4, April 2023

Pages: 1921 - 1925

DOI: https://www.doi.org/10.21275/SR23427104104

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