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All Journal MATEMATIKA Jurnal Matematika
Djuwandi Djuwandi
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Mathematics

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Journal : Jurnal Matematika

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HUBUNGAN BENTUK-BENTUK KHUSUS K-ALJABAR HIPER IMPLIKATIF Ratna Kusuma Ayu; Djuwandi Djuwandi
Jurnal Matematika Vol 2, No 1 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

ABSTRAK.Setiap K-aljabar hiper dapat dipandang sebagai BCK-aljabar dimana peran operasi biner pada BCK-aljabar diambil alih oleh operasi hiper yang berlaku pada K-aljabar hiper. Operasi hiper merupakan pemetaaan dari himpunan ke keluarga himpunan sehingga operasi hiper yang berlaku pada K-aljabar merupakan generalisasi dari operasi biner yang berlaku pada BCK-aljabar. Dalam Tugas Akhir ini, akan dijelaskan Definition-Definition dan teorema-teorema dalam K-aljabar hiper, K-aljabar hiper implikatif, K-aljabar hiper implikatif kuat dan K-aljabar hiper implikatif lemah serta hubungan antara ketiganya.Kata kunci : K-aljabar hiper, K-ideal hiper, K-aljabar hiper implikatif lemah, K-aljabar hiper implikatif kuat.
ANALISIS HUBUNGAN ANTARA PERSAMAAN RICCATI DAN PERSAMAAN INTEGRAL VOLTERRA TIPE DUA AnasKhairur Rijal Rijal; djuwandi djuwandi
Jurnal Matematika Vol 3, No 4 (2014): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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In this paper, a method for finding solution of the Riccati equation is introduced. The Riccatiequation is the first order inhomogeneous nonlinear ordinary differential equation (ODE) that can always be transformed into a second order homogeneous linear ODE. Since, every initial value problem (IVP) of the second order linear ODEs can be transformed into a Volterra integral equation (IE) of the second type, evaluate this equation by approximate technique by means, the approximate solution of the Riccati equation can be found. The approximate technique of the Voterra IE has been describe before, is based on the Taylor series expansion and it’s modification of the method. Behind the Cramer’s rule, an approximate solution of the 2nd type Volterra IE is easily can be determine and so, the approximate solution of the Riccati equation can be found. Test example is given to get conclusion about accuracy of the method.
Co-Authors AnasKhairur Rijal Rijal Astuti, Nita Dwi Azhar Mubarok, Azhar Bambang Irawanto Dwi Budi Santoso Handayani, Rizky Jiwangga, Sesar Sukma Juwanda, Farikhin Kartono . Lucia Ratnasari Oktavia, Ayu Ratna Kusuma Ayu Robertus Heri Sulistyo Utomo Siti Khabibah Suryoto Suryoto