Monte Carlo Method to Solve Diffusion Equation and Error Analysis

Authors

  • Samir Shrestha Kathmandu University, Nepal

DOI:

https://doi.org/10.3126/jnms.v4i1.37113

Keywords:

Diffusion equation, Monte Carlo method, Root mean square error, Brownian motion

Abstract

Three different mathematical approaches for the evolution of diffusion equation are presented. The evolution process of the diffusion equation is explained by principle of conservation law, probability distribution procedure, and finally though stochastic differential equation (SDE) driven by Brownian motion. The Monte Carlo method is discussed to solve the diffusion equation by generating the normally distributed random numbers and the root mean square error is derived for the Monte Carlo method. The numerical solutions are computed for 1-dimensional diffusion equation and results are compared with exact solution. Finally, theoretical root mean square error is compared with the maximum error and the L2-error by increasing the number of simulated points.

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Author Biography

Samir Shrestha, Kathmandu University, Nepal

Department of Mathematics, School of Science

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Published

2021-05-14

How to Cite

Shrestha, S. (2021). Monte Carlo Method to Solve Diffusion Equation and Error Analysis. Journal of Nepal Mathematical Society, 4(1), 54–60. https://doi.org/10.3126/jnms.v4i1.37113

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Articles