Digital Library: No conditions. Results ordered -Date Deposited. 2024-03-28T21:23:43ZEPrintshttp://digilib.unila.ac.id/images/sitelogo.pnghttp://digilib.unila.ac.id/2017-02-27T07:49:15Z2017-02-27T07:49:15Zhttp://digilib.unila.ac.id/id/eprint/25794This item is in the repository with the URL: http://digilib.unila.ac.id/id/eprint/257942017-02-27T07:49:15Z
APLIKASI METODE ANALISIS TRANSFORMASI HOMOTOPI PADA PERSAMAAN u_t+(u^2 )_x+(u^2 )_xxx=0
ABSTRAK
Metode Analisis Transformasi Homotopi (HATM) merupakan kombinasi Metode Analisis Homotopi (HAM) dan Transformasi Laplace yang dapat digunakan untuk mencari solusi analitik dari persamaan diferensial parsial tak linear. Sebagai contoh kasus dipilih diferensial parsial tak linear yang berbentuk
u_t+(u^2 )_x+(u^2 )_xxx=0.
Metode Analisis Transformasi Homotopi (HATM) sangat efektif digunakan pada persamaan diferensial parsial tak linear karena akan tetap valid walaupun permasalahan tak linear mengandung sembarang parameter. Setelah melalui beberapa proses perhitungan solusi analitik diperoleh untuk h=-1 yaitu u(x,t)=x/(1+2t).
Kata kunci : Metode Analisis Transformasi Homotopy, Transformasi Laplace, Metode Analisis Homotopy, solusi analitik
ABSTRACT
Homotopy Analysis Transform Method (HATM) combines Homotopy Analysis Method (HAM) and Laplace Ttransform. It was used to solve especially non-linear partial differential equations. As a case study we choose an equation in the form of u_t+(u^2 )_x+(u^2 )_xxx=0.
Homotopy Analysis Transform Method (HATM) is effectively used in non-linear partial differential equation because it remains valid even if the non linear problem contains any parameters. After some calculation process, we found analytical solution u(x,t)=x/(1+2t) for h=-1.
Keywords: Homotopy Analysis Transform Method, Homotopy Analysis Method, Laplace transform, analytic solution
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