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All Journal Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) International Journal of Ethno-Sciences and Education Research
Wijayanti, Marwah Daud
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PENYELESAIAN PERSAMAAN POISSON MENGGUNAKAN METODE HOMOTOPI PERTUBASI Mashuri, Mashuri; Rahmi, Sulistiowati Nur; Wijayanti, Marwah Daud; Putri, Alviana Pratama
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 13 No 2 (2021): 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.2021.13.2.5028

Abstract

ABSTRACT. In this paper, we discuss the solution of the Poisson equation(∂^2 u)/(∂x^2 )+(∂^2 u)/(∂y^2 )+8u=0with the initial condition u(0,y)=sin⁡2y. We use the homotopy pertubation method to get the solution.. The homotopy pertubation method is a combination of the homotopy method and the pertubation method. The solution of the equation is assumed to be in the form of a power series. The result is by using the homotopy pertubation method for the diffution equation, the solution is the same with the exact solution. Keywords: Poisson equation, Pertubation Homotopy method, power series. ABSTRAK. Dalam makalah ini dibahas tentang penyelesaian persamaan Poisson(∂^2 u)/(∂x^2 )+(∂^2 u)/(∂y^2 )+8u=0,dengan syarat awalnya adalah u(0,y)=sin⁡2y, menggunakan metode homotopi pertubasi. Metoda homotopi pertubasi merupakan gabungan antara metode homotopi dan metode pertubasi. Solusi persamaan diasumsikan dalam bentuk deret pangkat. Hasilnya diperoleh bahwa dengan menggunakan metode homotopi pertubasi untuk persamaan Poisson, solusi yang diperoleh sama dengan solusi eksaknya.Kata kunci: Persamaan Poisson, metode homotopi pertubasi, deret pangkat .
Etnomathematic Analysis: Implementation Of The Ecentric Digraph In Determining The Ka'ba As Center Of The Earth Wijayanti, Marwah Daud; Munahefi, Detalia Noriza; Wijayanti, Kristina; Prabowo, Agung
International Journal of Ethno-Sciences and Education Research Vol. 2 No. 1 (2022): International Journal of Ethno-Sciences and Education Research (IJEER)
Publisher : Research Collaboration Community (Rescollacom)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijeer.v2i1.233

Abstract

The Rajaban tradition is a tradition of religious rituals as an expression of gratitude and moments to commemorate historical events, one of which is the change in the direction of Qibla from Baitul Maqdis to the Kaaba in Mecca. Based on these problems, in this article, it is shown by using the study of Graph Theory, namely the eccentric digraph to determine the center of the earth's region. Data processing is done by making the Kaaba and the seven continents on the earth's surface as a point on graph G and the side connecting the points is the distance (in km) with physical boundaries between them being considered non-existent. The results of the discussion show that the Kaaba in Mecca is the center of the earth's area with ec(v1) = 12,039 = rad(G).
Co-Authors Agung Prabowo Kristina Wijayanti Mashuri Mashuri Munahefi, Detalia Noriza Putri, Alviana Pratama Rahmi, Sulistiowati Nur