*Result*: Modelling Two-Dimensional Laplace Equation Using Monte Carlo Simulation: A Python Viewpoint.

*This article explores the application of Monte Carlo simulation to model the two-dimensional Laplace equation which is commonly used in the steady-state heat conduction problems. By using statistical random walk principles, the study develops a Python-based algorithm to approximate solutions for the Laplace equation having fixed boundary (Dirichlet) conditions. The methodology involves formulating probability-based steps, discretizing the equation, and simulating particle paths to estimate temperatures at each grid point. A Python program has been developed to automate this process which has been tested using a sample problem. The results showed excellent agreement with analytical solutions, achieving 98% accuracy with 2000 random walks per node. The findings highlight the trade-off between increased accuracy and computational effort, as accuracy improves with a higher number of random walks. This approach and the provided Python code offer researchers a framework for applying Monte Carlo methods to similar problems and thus illustrate the adaptability of Python for complex simulations. [ABSTRACT FROM AUTHOR]

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