Samsul, Justin (2024) Estimasi paramterer persamaan diferensial biasa dengan menggunakan metode kuadrat terkecil = Estimating parameters of ordinary diferensial equations using least squares method. Bachelor thesis, Universitas Pelita Harapan.
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Abstract
Dalam tugas akhir ini akan dibahas suatu masalah untuk mengestimasi parameter-parameter dari suatu persamaan diferensial biasa (PDB). Metode untuk mengestimasi parameter-parameter PDB akan memanfaatkan metode yang sama ketika mencari koefisien-koefisien dari persamaan regresi linier. Metode ini dikenal dengan istilah solusi kuadrat terkecil. PDB yang akan dibahas dalam tugas akhir ini adalah model Lotka-Volterra (LV), model "Susceptible, Infected and Recovered" (SIR) dan model Lorenz. Dalam tugas akhir ini juga akan dipilih beberapa himpunan parameter dari setiap model yang akan memberikan solusi yang berbeda secara kualitatif. Metode untuk mencari solusi model-model diatas adalah metode "Runge-Kutta Orde-4". Terdapat dua hampiran yang akan diggunakan untuk membentuk matriks solusi yaitu hampiran beda maju dan hampiran beda pusat. Hasil dari penelitian ini memberikan kesimpulan bahwa hampiran beda pusat memberikan estimasi parameter yang lebih akurat pada ketiga model berikut. Secara umum metode dalam penelitian ini sudah cukup baik dalam mengestimasi parameter PDB dan dapat diggunakan untuk memodelkan data yang diambil di lapangan. / In this thesis we will discuss a problem for estimating parameters of an ordinary differential equation (ODE). The method for estimating ODE parameters is the same method as one that estimates the coefficients of a linear regression. This method is known as the least squares method. The ODE which will be discussed in this thesis are the Lotka-Volterra (LV) model, "Susceptible, Infected and Recovered" model and Lorenz model. Several sets of parameters from each model will also be selected to provide qualitatively different solutions. Numerical methods for finding the solution of each model is the "Runge-Kutta Order-4" method. There are two approaches which will be used to form the solution matrix, namely the forward difference approximation and the central difference approximation. Our research concludes that central difference approximation provides more accurate parameter estimation in these three models. In general, method in this research is reliable in estimating ODE parameters and can be used to model data taken from the real scenario.
Item Type: | Thesis (Bachelor) | ||||||||||||
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Uncontrolled Keywords: | regresi linier; pdb; solusi kuadrat terkecil; runge-kutta orde-4; lv; sir; lorenz | ||||||||||||
Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | University Subject > Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics Current > Faculty/School - UPH Karawaci > Faculty of Science and Technology > Mathematics |
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Depositing User: | Justin Samsul | ||||||||||||
Date Deposited: | 02 Feb 2024 07:46 | ||||||||||||
Last Modified: | 02 Feb 2024 07:50 | ||||||||||||
URI: | http://repository.uph.edu/id/eprint/61391 |
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