PENYELESAIAN PERSAMAAN POISSON MENGGUNAKAN METODE HOMOTOPI PERTUBASI

(SOLUTION OF THE POISSON EQUATION USING THE PERTUBATION HOMOTOPY METHOD)

  • Mashuri Mashuri Department of Mathematics, Jenderal Soedirman University
  • Sulistiowati Nur Rahmi Department of Mathematics, Jenderal Soedirman University
  • Marwah Daud Wijayanti Department of Mathematics, Jenderal Soedirman University
  • Alviana Pratama Putri Department of Mathematics, Jenderal Soedirman University

Abstract

ABSTRACT. In this paper, we discuss the solution of the Poisson equation
(∂^2 u)/(∂x^2 )+(∂^2 u)/(∂y^2 )+8u=0
with 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 .

Published
2021-12-07
How to Cite
MASHURI, Mashuri et al. PENYELESAIAN PERSAMAAN POISSON MENGGUNAKAN METODE HOMOTOPI PERTUBASI. Jurnal Ilmiah Matematika dan Pendidikan Matematika, [S.l.], v. 13, n. 2, p. 105-112, dec. 2021. ISSN 2550-0422. Available at: <http://jos.unsoed.ac.id/index.php/jmp/article/view/5028>. Date accessed: 20 apr. 2024. doi: https://doi.org/10.20884/1.jmp.2021.13.2.5028.

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