Diskretisasi model reaksi-difusi (Turing) dengan metode beda hingga eksplisit

Efendi, Ernawati (2013) Diskretisasi model reaksi-difusi (Turing) dengan metode beda hingga eksplisit. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA:

Diskretisasi model merupakan prosedur transformasi model kontinu ke model diskret. Diskretisasi dilakukan dengan menggunakan metode beda hingga maju (Forward Finite Difference), yaitu dengan menganalogikan persamaan diferensial yang menggunakan aturan limit, dengan persamaan beda yang menggunakan beda antar titik waktu diskret. Model yang digunakan dalam skripsi ini adalah model reaksi-difusi (Turing) yang merepresentasikan difusi cairan di dalam sel yang menyebabkan sel-sel bergerak.

Parameter-parameter yang digunakan dalam Model Reaksi-Difusi (Turing) yaitu, panjang domain yang tumbuh secara eksponensial L(t) = 1, tingkat pertumbuhan domain ρ = 0,01;0,001;0,0001, energi kinetik α = 0,9 dan b = 0,1 serta rasio koefisien difusi d = 0,06

Metode beda hingga merupakan metode numerik yang dapat digunakan untuk menyelesaikan persamaan diferensial parsial. Metode beda hingga yang digunakan yaitu metode beda hingga skema eksplisit, beda maju untuk waktu dan beda pusat untuk ruang. Dideskripsikan bahwa dengan metode beda hingga skema eksplisit diperoleh penyelesaian yang stabil dan mendekati solusi analitik. Bentuk diskret yang diperoleh yaitu :
u_i^n+1 = λu_i+1^n + (1-2λ)u_i^n + λu_i-1^n + ∆t(α-u_i^n(v_i^n)^2 - ρ u_i^n)
v_i^n+1 = dλv_i+1^n + (1-2dλ)v_i^n + dλv_i-1^n + ∆t(b+u_i^n(v_i^n)^2 - v_i^n - ρ v_i^n)
Berdasarkan solusi numerik yang diperoleh maka besarnya tingkat pertumbuhan domain (ρ) tidak berpengaruh terhadap perilaku dinamik model reaksi-difusi (Turing).

ENGLISH:

Discretization model is a continuous model transformation procedure to discrete model. Discretization is done using advanced finite difference method, by analogy differential equations using limit rules, with different equations using the different between discrete time points. The model used in this paper is a model of reaction-diffusion (Turing) that represents the diffusion of fluid in the cells that cause the cells to move.

The parameters used in the reaction-diffusion model (Turing), thedomain length grows exponentially L(t) = 1, the domain growth rate ρ = 0,01;0,001;0,0001, the kinetic energy of α = 0,9 and b = 0,1 and the ratio of the diffusion coefficient d = 0,06

Finite difference method is a numerical method that can be used to solve partial differential equations. Methods used explicit finite difference scheme developed for the time difference and central difference for the space to complete the reaction-diffusion equation (Turing). Described the resolution obtained with this method is stable and close to analytic solutions discrete models obtained is:
u_i^n+1 = λu_i+1^n + (1-2λ)u_i^n + λu_i-1^n + ∆t(α-u_i^n(v_i^n)^2 - ρ u_i^n)
v_i^n+1 = dλv_i+1^n + (1-2dλ)v_i^n + dλv_i-1^n + ∆t(b+u_i^n(v_i^n)^2 - v_i^n - ρ v_i^n)
Based on the numerical solution obtained then the amount of domain growth (ρ) does not affect the stability of reaction-diffusion models (Turing).

Item Type: Thesis (Undergraduate)
Supervisor: Pagalay, Usman and Kusumastuti, Ari
Keywords: Diskretisasi Model Reaksi-Difusi (Turing); metode beda hingga skema eksplisit; model kontinu; model diskret; discretization, reaction-diffusion (Turing) model, forward finite differences method; continuous model; discrete model
Subjects: 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010206 Operations Research
01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified
01 MATHEMATICAL SCIENCES > 0199 Other Mathematical Sciences > 019999 Mathematical Sciences not elsewhere classified
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Ahmad Zaini
Date Deposited: 13 Jun 2017 03:59
Last Modified: 13 Jun 2017 03:59
URI: http://etheses.uin-malang.ac.id/id/eprint/7092

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