Browsing by Author "Imran, M."

Now showing 1 - 8 of 8
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    CARA LAIN MENENTUKAN TAKSIRAN ERROR UNTUK METODE INTEGRAL NUMERIK
    (2014-03-25) Wati, D. S.; Imran, M.; Deswita, L.
    This paper discusses a technique to estimate an error in numerical integration methods, which is a review and an expansion, as well as partial correction from the article Peter R. Mercer [The College Mathematics Journal, 36 (2005): 27-34]. After obtaining the error estimates of the numerical integration methods for a single interval, composite error estimate forms are developed, which are only dependent on the first derivatives of the function. By comparing the error estimates obtained with error estimates obtained by polynomial interpolation error, it is visible that the error estimates obtained for the trapezoidal method and the midpoint method are sharper. This finding does not apply to the Simpson method.
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    METODE DEKOMPOSISI ADOMIAN UNTUK MENYELESAIKAN PERSAMAAN PARABOLIK
    (2013-06-25) Marbun, Ester G.; Imran, M.; Pane, Rolan
    We discuss the application of Adomian decomposition method to solve a parabolic differential equation which is a review as well as fix of some errors contained in the article of Javidi and Golbabai entitled Adomian decomposition method for ap- proximating the Solution of Parabolic Equations [5]. Then, to see the accuracy of the discussed method, we compare the solutions in the form of series obtained by Adomian decomposition method with the exact solution of two parabolic differ- ential equations. The results indicate that the solutions obtained using Adomian decomposition method is very accurate.
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    METODE ITERASI BEBAS TURUNAN BERDASARKAN KOMBINASI KOEFISIEN TAK TENTU DAN FORWARD DIFFERENCE UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR
    (2013-06-10) Mahrani; Imran, M.; Agusni
    We discuss an iterative method to solve a nonlinear equation, which is free from derivatives by approximating a derivative in the two-step Newton method by the method of undetermined coefficients and forward difference. We show analytically that the method is of three orde for a simple root. Numerical experiments show that the new method is comparable with other discussed methods.
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    METODE ITERASI DUA LANGKAH BEBAS TURUNAN BERDASARKAN INTERPOLASI POLINOMIAL
    (2014-03-25) Monti, N. D.; Imran, M.; Karma, A.
    This paper discusses a technique based on an interpolating polynomial to approximate a derivative appearing in the two-step iterative method, so that a two-step iterative method free from derivative is obtained. It is shown analytically that this iterative method is of order three for a simple root. Numerical experiments show that the proposed method converges to a simple root faster than the other mentioned methods
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    METODE ITERASI TANPA TURUNAN BERDASARKAN EKSPANSI TAYLOR UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR
    (2014-03-25) Yuliani, Evi; Imran, M.; Putra, S.
    This paper discusses free derivative iterative methods based on a Taylor expansion to solve a nonlinear equation. It is analytically shown that the methods are the third order. Numerical comparisons among the proposed iterative methods, Chebyshev method, Halley method, and Chebyshev-Halley method show that the proposed methods are better in performance, in terms of succeeding in obtaining the root.
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    METODE ORDE-TINGGI UNTUK MENENTUKAN AKAR DARI PERSAMAAN NONLINEAR
    (2013-05-28) Edwar, I.P.; Imran, M.; Deswita, L.
    We discuss a derivation of a high-order iterative method based on Taylor expansion of a nonlinear function. The method is a special case of the method derived by Germani, A., et al. in Journal of Optimization Theory and Applications. 131 (2006). 347-364. We show analytically with a different technique from those of Germani that the method is of four order. The numerical simulation using four nonlinear functions shows that the performance of the method is better than those of Newton method, Traub method, Halley method, and Chebyshev method.
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    METODE RUNGE KUTTA ORDE-4 DENGAN KONTROL GALAT
    (2013-03-16) Juita, Nurma; Imran, M.; Kho, Johannes
    This paper discusses the Runge Kutta method of order-4 (RK (4,4)) with an error control, which is a combination of the Runge Kutta method of order-4 based on an Arithmetic mean (RKAM-4) and the Runge Kutta method of order-4 based on a Contraharmonic mean (RKCoM-4). Difference between approximation of RKAM-4 and RKCoM-4 is used to control the step length of the method. So the RK(4,4) is a method with a variable step length, as well as the Runge Kutta Fehlberg 4(5) (RKF4(5)). Numerical computation is also done in four cases, which are then compared with RKF4(5). The results show that the behavior of RK (4,4) is similar to that of RKF4(5)
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    METODE SIMPSON-LIKE TERKOREKSI
    (2014-03-25) Suryani, Ilis; Imran, M.; Karma, Asmara
    This paper discusses a derivation of the corrected Simpson-like method using a difference operator to approximate a definite integral, as a review of the article Ujevi ́, N. & A. J Roberts [ANZIAM Journal, 45 (2004): 41–56]. The computational c results show that the corrected Simpson-like method is better than Simpson method that is the method is exact for a fifth-order polynomial