scholarly journals Solusi Numerik Model SIR pada Penyebaran Penyakit Hepatitis B dengan Metode Perturbasi Homotopi di Provinsi Sulawesi Selatan

2020 ◽  
Vol 3 (2) ◽  
pp. 79
Author(s):  
Syafruddin Side ◽  
Maya Sari Wahyuni ◽  
Muh. Rifki
Keyword(s):  
Hepatitis B ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Health Department ◽  
Sir Model ◽  
Homotopy Perturbation ◽  
South Sulawesi ◽  
Numeric Simulation ◽  
Hepatitis B Treatment ◽  
Numeric Solution

Penelitian ini membahas mengenai solusi secara numerik dari model SIR pada penyebaran penyakit Hepatitis B dengan Metode Perturbasi Homotopi. Data yang digunakan adalah data sekunder dari penelitian Rosdiana (2015) yang berupa model SIR dan jumlah penderita Hepatitis B di Provinsi Sulawesi Selatan tahun 2015 dari Dinas Kesehatan Provinsi Sulawesi Selatan. Pembahasan dimulai dari penentuan solusi umum dengan Metode Perturbasi Homotopi, penentuan parameter, simulasi dan analisis hasil. Setelah dilakukan analisis dari simulasi numerik terlihat bahwa Metode Perturbasi Homotopi dapat digunakan untuk melihat kecenderungan perlakuan penyakit Hepatitis B di Provinsi Sulawesi Selatan dan menjadi bahan pertimbangan untuk tindakan pencegahan penyakit Hepatitis B. Dalam penelitian ini diperoleh grafik pergerakan dari model SIR dengan data riil.Kata kunci : Solusi Numerik, Model SIR, Hepatitis B, Metode Perturbasi Homotopi, PemodelanThis research aims  to find out the numerical solustion from a SIR model on the spread of Hepatitis B by Homotopy Perturbation Method. This research used a secundary data from Rosdiana’s research (2015)  focused on SIR model and number of Hepatitis B in South Sulawesi 2015 from Health Department of South Sulawesi. The discussion started by determining general solution with Homotopy Perturbation Method, parameter decision, simulation and result analyzis. After conducting an analyzis from numeric simulation it shows that the Homotopy Perturbation Method can be used to analyze the preference of Hepatitis B treatment in South Sulawesi also can be a consideration for preventing action of infectious disease of Hepatitis B. This research gets movement grafic and result analyzis from SIR model by riil data.Keywords : Numeric Solution, SIR Model, Hepatitis B, Homotopy Perturbation Method, Modeling

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

A new modification of the homotopy perturbation method

2021 ◽  
pp. 095745652199987
Author(s):  
Magaji Yunbunga Adamu ◽  
Peter Ogenyi
Keyword(s):  
Comparative Analysis ◽  
Error Analysis ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Oscillators ◽  
Absolute Error ◽  
New Method ◽  
Optimal Analysis ◽  
Homotopy Perturbation ◽  
Accuracy And Precision

This study proposes a new modification of the homotopy perturbation method. A new parameter alpha is introduced into the homotopy equation in order to improve the results and accuracy. An optimal analysis identifies the parameter alpha, aimed at improving the solutions. A comparative analysis of the proposed method reveals that the new method presents results with higher degree of accuracy and precision than the classic homotopy perturbation method. Absolute error analysis shows the convenience of the proposed method, providing much smaller errors. Two examples are presented: Duffing and Van der pol’s nonlinear oscillators to demonstrate the efficiency, accuracy, and applicability of the new method.

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

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