Value of lambda, ×’ for crank-nicolson scheme on solving diffusion equation

Choon, Lee Meng (2007) Value of lambda, ×’ for crank-nicolson scheme on solving diffusion equation. Universiti Malaysia Sabah. (Unpublished)

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Abstract

The main purpose of this study is to investigate if a specific value of lambda, ג. = k(Δt)) exists where M, Δt , Δx, k, p and C p represent time step, length 2pCp(Δx) ² increment in x direction, coefficient thermal diffusivity, density and specific heat, respectively. The specific value is able to achieve the most desirable approximate solution for any combination of M and Ax base on the Crank-Nicolson scheme. A basic diffusion equation is discretized by Crank-Nicolson scheme and the tridiagonal matrix system is solved by Crout decomposition algorithm. All the data have been processed by diffusion equation being use in analysis to compare with the analytical solution. The specific value of the A. is not exist for any combination of Δt and Δx. However, the study resulted that a value of A. is happened to exist for each Δt = 0.3Δx which is able to ensure the approximate solution executed in the highly accuracy.

Item Type: Academic Exercise
Uncontrolled Keywords: value of lambda, Crank-Nicolson scheme, accuracy, time step, coefficient thermal diffusivity
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: SCHOOL > School of Science and Technology
Depositing User: MDM SITI AZIZAH IDRIS
Date Deposited: 08 Jan 2014 05:53
Last Modified: 10 Oct 2017 08:28
URI: http://eprints.ums.edu.my/id/eprint/8004

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