Skema Prediktor-Korektor Untuk Solusi Numerik Persamaan Good Boussinesq

Ardhini, Julita Ayu (2018) Skema Prediktor-Korektor Untuk Solusi Numerik Persamaan Good Boussinesq. Sarjana thesis, Universitas Brawijaya.

Abstract

Pada skripsi ini dibahas solusi numerik persamaan good Boussinesq nonlinear. Persamaan good Boussinesq merupakan persamaan diferensial parsial nonlinear yang umumnya sulit untuk ditentukan solusi analitiknya, sehingga perlu dilakukan pendekatan numerik. Konstruksi skema numerik yang dihasilkan merupakan skema beda hingga implisit nonlinear. Berdasarkan hasil dan pembahasan, skema beda hingga stabil dengan syarat dan memiliki kesalahan pemotongan orde empat terhadap waktu dan orde dua terhadap ruang. Untuk mendapatkan solusi numerik dari persamaan beda hingga implisit nonlinear diperlukan metode iterasi, dalam skripsi ini digunakan skema prediktor-korektor. Berdasarkan analisis kestabilan von Neumann, skema prediktor-korektor stabil bersyarat dengan rentang kestabilan lebih lebar daripada skema beda hingga. Dengan melakukan beberapa simulasi menggunakan nilai ukuran langkah spasial dan langkah temporal tertentu dapat ditunjukkan bahwa metode yang diusulkan cukup akurat.

English Abstract

This final project discusses numerical solutions of nonlinear good Boussinesq equation. Good Boussinesq equation is a nonlinear partial differential equation which is generally difficult to determine its analytical solution, so numerical approximation is needed. The result of numerical scheme construction is a nonlinear implicitly finite difference scheme. Based on the results and discussion, the proposed finite difference scheme is conditionally stable and the truncation error is fourth order accurate to time and second order accurate to space. Iteration method is needed to get the solution of nonlinear implicity finite difference. In this final project a predictor-corrector scheme is implemented. From the results of von Neumann stability analysis, the predictor-corrector scheme is conditionally stable with the stability range is wider than finite difference scheme. By take some simulations using the spatial step size and temporal step size it can be shown that the proposed method is quite accurate.

Other obstract

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Item Type: Thesis (Sarjana)
Identification Number: SKR/MIPA/2018/284/051807044
Uncontrolled Keywords: persamaan good Boussinesq, skema prediktor-korekto, Boussinesq equations, predictor-corrector schemes
Subjects: 500 Natural sciences and mathematics > 518 Numerical analysis > 518.5 Numerical approximation
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika
Depositing User: Nur Cholis
Date Deposited: 11 Jun 2020 00:53
Last Modified: 22 Oct 2021 08:30
URI: http://repository.ub.ac.id/id/eprint/168451
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