Azizah, Siti Shifatul (2012) Diskretisasi model Lorenz dengan analogi persamaan beda. 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 analogi persamaan beda, yaitu dengan menganalogikan persamaan diferensial yang menggunakan aturan limit, dengan persamaan beda yang menggunakan beda h antar titik waktu diskret. Model yang digunakan dalam skripsi ini adalah model Lorenz yang merepresentasikan aliran konveksi udara di atmosfer yang terjadi karena perbedaan suhu.
Inti dari penelitian ini adalah melakukan konstruksi model diskret Lorenz dan pengamatan perbandingan perilaku antar model diskret dan model kontinu. Metode yang digunakan terdiri dari tiga tahap, yaitu tahap konstruksi untuk kasus diskret, tahap diskretisasi masing-masing persamaan dan tahap validasi model diskret dengan membandingkan hasil simulasi grafik kontinu dan diskret.
Hasil dari penelitian ini didapatkan model diskret Lorenz dalam bentuk umum: Χm+1=(1-σh) Xm+σhYm, Ym+1=(R-Zm)hXm + (1-h)Ym, Zm+1=(1-bh)Zm + hXmYm dengan m Є N dan h → 0. Perbandingan perilaku setiap variabel pada model kontinu dan diskret diamati saat h=0,1;0,01;0,001;0,0001 dengan parameter σ=10 dan Ь=8/3 dan r=28 nilai awal (Xo,Yo,Zo)=(1,1,1). Untuk semakin kecil perbedaan antara model kontinu dan diskret akan semakin sedikit pula. Dari hasil simulasi diskret, efek chaos terjadi pada t≥15 menit. Saat, h≤0.001 model diskret yang dibentuk dapat mengimplementasikan perilaku variabel kontinu dan gejala kekacauan (chaos) di sekitar titik kesetimbangan.
ENGLISH:
Discretization of model is transformation a model in continuous form to be a discrete one. It does to get a model which applicative in continuous and discret condition. It can be done by using difference equation analogy method. It analogues a differential equation that use limit rules with difference equation that use difference between the points of discrete time. The model in this research is Lorenz model. This model represents a convection motion in atmosphere that occurs due to temperature difference.
The purpose of the research is show construction the discrete version of Lorenz model and know comparison of discrete Lorenz behavior and continuous one. This research was done by three steps. First, construct time for discrete case. Second, discretization each of equations in Lorenz system, and third, validation the discrete model that is obtained, by simulating its graphics and compare it with continuous one.
The results of this research obtain a discrete Lorenz model in general form: ... with ... and ... . Comparison of the behavior of each variables on a continuous and discrete model is observed when with the parameter and and initial value. For smaller the difference between continuous and discrete model will be less too. From, simulation of discrete graphics, chaotic behavior can be shown from minutes. When, discrete model can implement the behavior of continuous variables and chaotic behavior around equilibrium point.
Item Type: | Thesis (Undergraduate) | |||||||||
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Supervisor: | Pagalay, Usman and Nashichuddin, Achmad | |||||||||
Contributors: |
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Keywords: | Diskretisasi; Model Lorenz; Persamaan Beda; Model Kontinu; Model Diskret; Chaos; Discretization; Lorenz Model; Difference Equation; Continuous Model; Discrete model | |||||||||
Departement: | Fakultas Sains dan Teknologi > Jurusan Matematika | |||||||||
Depositing User: | Nanum Sovia | |||||||||
Date Deposited: | 23 May 2017 10:51 | |||||||||
Last Modified: | 23 May 2017 10:51 | |||||||||
URI: | http://etheses.uin-malang.ac.id/id/eprint/6697 |
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