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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Prosiding BAREKENG: Jurnal Ilmu Matematika dan Terapan MAJAMATH: Jurnal Matematika dan Pendidikan Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Jurnal Galam Jurnal Siger Matematika Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Matematika Integratif AMMA : Jurnal Pengabdian Masyarakat
Rina Reorita
Jurusan Matematika, Universitas Jenderal Soedirman
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ANALISIS DINAMIK MODEL LESLIE-GOWER DENGAN PENGARUH WAKTU TUNDA DAN PEMANENAN PROPORSIONAL Kemalasari, Azhari; Reorita, Rina; Renny, Renny
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 14 No 1 (2022): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2022.14.1.5898

Abstract

ABSTRACT. The main purpose of this research is to study the Leslie-Gower model with time delay and proportional harvesting. The model is solved qualitatively by analyzing the stability around equilibrium points. The Leslie-Gower with delay time and proportional harvesting have four equilibrium points. There is an unstable equilibrium point and a stable equilibrium point. Meanwhile, the stability of the other two equilibrium points depends on the value of the parameters taken. The parameter of delay time causes the solution to oscillate. The greater the delay time value used the greater amplitude of oscillations in the system. It means the model will take longer to stabilize.Keywords: Model Leslie-Gower, equilibrium points, time delay. ABSTRAK. Penelitian ini dilakukan untuk menganalisis perilaku model Leslie-Gower dengan waktu tunda dan pemanenan proporsional. Metode yang digunakan pada penyelesaian model adalah metode kualitatif, yaitu dengan menganalisis kestabilan titik kesetimbangan model. Model Leslie-Gower dengan waktu tunda dan pemanenan proporsional memiliki empat titik kesetimbangan. Terdapat satu titik kesetimbangan tidak stabil dan satu titik kesetimbangan yang bersifat stabil. Sementara itu, untuk dua titik kesetimbangan lainnya, bergantung pada nilai parameter yang diambil. Waktu tunda mengakibatkan adanya osilasi pada model. Semakin besar nilai waktu tunda yang digunakan, maka semakin besar pula simpangan pada osilasi yang terjadi pada penyelesaian sistem. Hal tersebut mengakibatkan model akan semakin lama untuk menuju kestabilan.Kata Kunci: Model Leslie-Gower, titik kesetimbangan, waktu tunda.
ON THE THIRD ORDER SOLUTION OF KdV EQUATION BY USING HOMOTOPY PERTURBATION METHOD Mashuri, Mashuri; Zakiyah, Yayah; Reorita, Rina
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 2 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss2pp0609-0614

Abstract

In this research we discussed about the solution of the KdV equation using Homotopy Perturbation method. The KdV equation that describing water wave equation solved by using the mixing method between Homotopy and Perturbation method. Homotopy was built with embedding parameter p∈[0,1] which undergoes a deformation process from linear problems to nonlinear problems and the assumed solution of the KdV equation is expressed in the form of a power series p up to the third order. The result show that in each order solution we obtained resonance term. for handling the condition, we used Lindsteadt-Poincare method.the wave number k2 and dispersion relation can be obtained in the second order solution as the effect of using Lindsteadt-Poincare method.
Co-Authors Afni Atika Marpaung Agik Dwika Putra Agustini Tripena Azhari Kemalasari Budi Mulyana, Budi Danar Agus Nugroho Idha Sihwaningrum Idha Sihwaningrum Ilham Satria Raditya Putra Kemalasari, Azhari Kurniasih, Laely Laely Kurniasih Mashuri Mashuri Mashuri Mashuri Mashuri Mashuri Muhamad Faqih Hidayatullah Muhammad Okky Ibrohim Mutia Nur Estri Mutia Nur Estri, Mutia Nur Niken Larasati Niken Larasati Niken Larasati Nunung Nurhayati Nunung Nurhayati Puspita Intan Sari Renny Renny Renny Renny Renny Renny Renny Ris Hadi Purwanto Siti Rahmah Nurshiami, Siti Rahmah Sri Maryani Sulistyoningrum, Tri Puji Susi Agustianingsih Tri Puji Sulistyoningrum Winda Triyani Zakiyah, Yayah