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Ririn Sulpiani
Diponegoro University
Mathematics

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Solusi Numerik Persamaan Difusi dengan Menggunakan Metode Beda Hingga Sulpiani, Ririn; Widowati, Widowati
JURNAL SAINS DAN MATEMATIKA Volume 21 Issue 3 Year 2013
Publisher : JURNAL SAINS DAN MATEMATIKA

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Abstract

The developmental process characteristic of the distribution of pressure, enthalpy and temperature on geothermal reservoir can be represented in mathematical models.The basic equation used in the modeling process is the Darcy law and mass equilibrium equations with the physical parameters of the distribution of pressure. Pressure distribution model obtained is a two-dimensional diffusion equation in the form of two-order partial differential equations. Furthermore, the finite difference centered method used to find the numerical solution of the  diffusion equation.   Keywords: Geothermal Reservoir, pressure, Darcy law, finite difference method
Solving a system of linear equations by QR Factorization Method for Temperature and Altitude Regression Model against Spontaneous-Potential Widowati, Widowati; Setyawan, Agus; Mustafid, Mustafid; Nur, Muhammad; Sudarno, Sudarno; Harmoko, Udi; Adhy, Satriyo; Gunawan, Gunawan; Subagio, Agus; Tjahjana, Heru; Sulpiani, Ririn; Riyanto, Djalal Er; Suhartono, Suhartono; Mukid, Mochammad Abdul; Suseno, Jatmiko Endro
JURNAL SAINS DAN MATEMATIKA Volume 22 Issue 3 Year 2014
Publisher : JURNAL SAINS DAN MATEMATIKA

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Abstract

Many real problems can be represented in the form of multiple linear regression equation. One of those is the relationship between the variables of temperature and altitude of the spontaneous-potential. In order to determine the parameters of the regression equation, the least squares method was used. From here, there was obtained the system of linear equations. In this paper, to solve systems of linear equations, the exact method was used as the exact solution is certainly better than the approached solution. The method used was the QR factorization method. At the QR factorization, the system of linear equations was written in form of matrix equation. Then, the coefficient matrix which the number of rows is m and number of columns is n with linearly independent columns was factored into the matrix Q which has the same size with the matrix A, with orthonormal columns and matrix R was upper triangular. Furthermore, by backward substitution, it could be obtained the exact solution of linear equation system. As verification of this proposed method, a case study was given using data of temperature, altitude, and spontaneous-potential in the geothermal manifestations area, Gedongsongo, Mount Ungaran Semarang. From here, it was obtained the parameters of exact multiple linear regression model which states the relationship between temperature and altitude toward the spontaneous-potential.
Co-Authors Agus Setyawan Agus Subagio Djalal Er Riyanto I Gusti Ngurah Antaryama Jatmiko Endro Suseno Moch. Abdul Mukid Muhammad Nur Mustafid Mustafid Redemtus Heru Tjahjana Satriyo Adhy Sudarno Sudarno Udi Harmoko Yundari, Yundari