Febrian, Haris (2014) Skema Beda Hingga Orde Empat Untuk Persamaan Good Boussinesq. Sarjana thesis, Universitas Brawijaya.
Abstract
Pada skripsi ini, persamaan Good Boussinesq nonlinear ditransformasikan ke dalam sistem persamaan diferensial orde satu. Secara umum solusi analitik dari persamaan Good Boussinesq nonlinear sulit untuk ditentukan sehingga perlu dilakukan pendekatan numerik. Skema numerik yang digunakan dalam skripsi ini adalah skema beda hingga yang diperoleh dari pendekatan Pad ́. Berdasarkan hasil dan pembahasan diperoleh kesalahan pemotongan dari skema numerik adalah orde empat untuk ruang, orde dua untuk waktu dan stabil tanpa syarat. Teknik linearisasi digunakan untuk memudahkan simulasi numerik dari skema nonlinear sistem persamaan Good Boussinesq. Hasil simulasi numerik menunjukkan bahwa interaksi dua gelombang sensitif terhadap nilai amplitudo di mana solusi blow up terjadi jika nilai amplitudo awal relatif besar.
English Abstract
In this paper the nonlinear Good Boussinesq equation is transformed into a system of first order differential equations. The analytical solution of the nonlinear Good Boussinesq equation is generally difficult to be determined so that it needs a numerical approximation. Numerical scheme wich is used in this paper is a finite difference scheme obtained from Pad ́ approximation. It is shown that numerical scheme is fourth order accurate in space, second order accurate in time and is unconditionally stable. Linearization technique is used to ease the numerical simulation of nonlinear Good Boussinesq equations system scheme. Numerical simulation results show that the interaction of the two waves are sensitive toward the value of the amplitude where the blow up solution occurs if the initial amplitude is relatively large.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/MIPA/2014/393/051407780 |
| Subjects: | 500 Natural sciences and mathematics > 510 Mathematics |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika |
| Depositing User: | Budi Wahyono Wahyono |
| Date Deposited: | 24 Nov 2014 07:32 |
| Last Modified: | 21 Oct 2021 06:38 |
| URI: | http://repository.ub.ac.id/id/eprint/154033 |
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