Computational Solution of One Dimensional Diffusion Equation with Fixed Limits
Published: 2021
Author(s) Name: Alpna Mishra |
Author(s) Affiliation: Department of Mathematics, SBSR, Sharda University, Greater Noida, Uttar Pradesh, India
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Abstract
This paper presents a model for the mathematical description of the diffusion process, as well as an attempt to use Green’s function approach to solve the one-dimensional diffusion equation within the necessary bounds. By studying the initial condition for, we will be able to obtain the appropriate solution to this diffusion equation. With a constant diffusion coefficient, this equation represents the rate of change of concentrations of substances in their own lattice or in separate substances. Finally, numerical answers will be obtained via a computational approach. Because we consider t = 0 throughout the equation, the result can also be applied to an isothermal diffusion.
Keywords: Diffusion process, Ficks law, Green’s function method, Mathematical modelling of diffusion process, Thermal diffusion.
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