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All Journal Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam
Imran M.
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Mathematics

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METODE ITERASI BERTIPE NEWTON UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR DENGAN ORDE KONVERGENSI SEBARANG BILANGAN BULAT Putri, Ayunda; M., Imran; ', Aziskhan
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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Abstract

This article discusses an analytic study of combining iterative methods of order p and q with p and q integers to Newton’s method to obtain a Newton-type iteration method of order p + q. This new method can also be applied to solve systems of nonlinear equations. Numerical computations are carried out consecutively for a method of second and third order, which produce a Newton-type method of fifth order, and methods of third and fifth order, which produce a Newton-type method  of eighth order. The test results support the analytical studies.
METODE ITERASI OPTIMAL BERORDE EMPAT UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR Yanti, Helmi Putri; M., Imran; Pane, Rolan
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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In this article, we discuss the derivation of an optimal iterative method using a quadratic polynomial, which is a review and a correction of a part of Fern´andez-Torres and V´asquez-Aquino’s article [Advances in Numerical Analysis, 10: 1-8, 2013]. Analytically we show that the obtained method has an order of convergencefour and requires three function evaluations per iteration, so that the efficiency index of the method is 1.587. The analytical results are in agreement with the com-putational examples. Numerical comparisons show that the method obtained can compete with the existing fourth order methods.
SOLUSI POLINOMIAL TAYLOR PERSAMAAN DIFERENSIAL-BEDA LINEAR DENGAN KOEFISIEN VARIABEL Nurjanah, Siti; M., Imran; M., Musraini
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses how to obtain the Taylor polynomial solution of a higher order linear differential and difference equation with variable coefficients whose initial conditions are known. The process begins by assuming the solution of a higher order linear differential and difference equation in the form of polynomial Taylor. Then it is followed by presenting this equation and its initial conditions in the form of a matrix. This matrix is changed into an augmented matrix. Taylor polynomialsolutions of a higher order linear differential and difference equations is obtained by solving the augmented matrix using elementary row operations.
PERBAIKAN METODE ITERASI YA NG DIPERKE NALKAN YOONMEE HAM UNTUK MENYELESAIKAN PE RSAMAAN NONLINEAR Mis Mayra; Imran M.; Aziskhan '
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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We discuss an improvement of metho d prop osed by Ham, Y. [Applied Mathematics and Computational. 222: 477–486. 2008]. Analytically we show that by adding some conditions on the weight functions, the prop osed metho d is of order five or six. Numerical comparison shows that the prop osed iterative metho ds with different weight functions do not have significant differences in terms of the number of iteration in obtaining the root.
FAMILI METODE ITERASI BERORDE TIGA UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR Dewi Kusuma; Imran M.; Zulkarnain '
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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We discuss a family of iterative methods derived by giving a weight function recur-sively to the corrector of Newton’s method, which is a review of article of Herceg and Herceg publised on [Applied Mathematics and Computation, 87 (2010), 2533–2541]. Weighting with a specific index produces Super-Halley’s method. Analytically it is shown that the order of the convergence of the method is three. Furthermore, this iteration method requires four function evaluations per iteration, so its efficiency index is 1.316. Then, computational tests show that the discussed method is better than Newton’s method, and does not have significant differences with Super Halley’s method in terms of error produced.
METODE ITERASI BARU YANG OPTIMAL BERORDE EMPAT TANPA TURUNAN KEDUA DAN DINAMIKNYA Fitria Afri Yanti; Imran M.; Agusni '
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses an iterative metho d to solve a nonlinear equation, which is free from second derivative by approximating a second derivative by a divided difference. Analytically it is shown using the Taylor expansion and geometric series that this iterative metho d has a convergence of order four. Furthermore, numerical comparisons between the prop osed metho d and several well-known iterative methods of order four and free from second derivative are p erformed. By varying the initial guesses, we compare the numb er of iterations obtained by those methods to get an approximated ro ot. In addition, comparisons are also made through basins of attraction of the discussed methods.
METODE KUADRAT TERKECIL BERBOBOT DAN APLIKASINYA PADA MODEL MATEMATIKA KONSUMSI BENSIN Riris Siagian; Imran M.; Supriadi Putra
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses the application of the least squares and weighted least squares method to determine the amount of fuel consumption at a given distance in the use of vehicles in and out of town at the same time using mathematical models. This articleis a review of Izzo’s article [Mathematics Magazine 73(3):226-231]. Computational examples using real data show that the solution given by the weighted least squares method to a mathematical model of gasoline consumption more in line with the real situation.
MODIFIKASI FAMILI METODE ITERASI MULTI-POINT UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR Yolla Sarwenda; Imran M.; Zulkarnain '
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses a modified family of multi-p oint iterative method, which is free from second derivative, obtained by mo difying the Chebyshev-Halley-type method. Analytically using Taylor expansion and geometric series, we show that the method has convergence order of three and four. Further by varying the value of the parameter in the formula, we obtain some third order iterative metho ds free secondderivative. Then using some test functions, the prop osed metho d is compared with several known multi-p oint iterative metho ds of order three and four.
VARIASI METODE CHEBYSHEV DENGAN ORDE KEKONVERGENAN OPTIMAL UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR Julia Murni; Imran M.; Sigit Sugiarto
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 1, No 2 (2014): Wisuda Oktober 2014
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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Abstract

This article discusses variants of Chebyshev's methods to solve a nonlinear equation. Analytically, it is shown that the methods are of four order. Numerical comparisons show that the proposed methods are better than Newton's method, Chebyshev's method, Chebyshev-Halley's method, and Jarratt's method in performance, in terms of succeeding in obtaining the root.
METODE BERTIPE STEFFENSEN DENGAN ORDE KONVERGENSI OPTIMAL UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR Sarbaini '; Imran M.; Asmara Karma
Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam Vol 2, No 1 (2015): Wisuda Februari 2015
Publisher : Jurnal Online Mahasiswa (JOM) Bidang Matematika dan Ilmu Pengetahuan Alam

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This article discusses a mo dification of a third order Steffensen-typ e method, by adding three different weight functions into the third order Steffensen-type method, so that we obtain three different correction Steffensen-typ e metho ds. These methods are of order three and require three function evaluations p er iteration so that their index of efficiency is 1.587. Computational results show the correction Steffensentype methods are competitive enough in their class.
Co-Authors ', Aziskhan Agusni ' Asmara Karma Ayunda Putri Aziskhan ' Bustami ' Dewi Kusuma Dina Oktavieny Fitria Afri Yanti Helmi Putri Yanti Irpan Riski Munte Julia Murni Mis Mayra Musraini M. Nurul Khoiromi Riris Siagian Risvi Ayu Imtihana Rolan Pane Romendiana ' Sarbaini Sarbaini Sigit Sugiarto Siti Nurjanah Supriadi Putra Yolla Sarwenda Zulkarnain '