Browsing by Author "Karma, Asmara"
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Item Keterbatasan Jari-Jari Spektral Suatu Matriks(2015-07-02) Karma, Asmara; M. NatsirMisalkan A =[ ajj] merupakan matriks kuadrat berukuran n x n dengan elemen bilangan kompleks, dan definisikaii P ( A ) merupakan jari-jari spektral dari A dan |A| merupakan matriks [ |ajj|]. A. Brawaer, W. Ledermann dan A. Ostrwski telah mengembangkan batasan untuk P ( A ) , sedangkan Perron dan Ferbenius tclah merumuskan batasan P ( A ) < P(|A|) yang merupakan batas bawah untuk P ( A ) yang mana tidak lebih besar dari P ( A ). Pada penelitian ini kita peroleh suatu barisan terbatas untuk p(A) didalam batas P(|Ar|), (r=1,2,3,…) yeng lebih besar atau sama dengan P( A) dan konvergen ke P ( A ) .Item METODE ITERASI BARU UNTUK MENYELESAIKAN PERSAMAAN NONLINEAR(2014-04-12) Putra, Supriadi; Kurniawati, Ria; Karma, AsmaraKita akan mendiskusikan sebuah metode iterasi baru untuk menyelesaikan persamaan nonlinear satu variabel. Tulisan yang sama telah dilakukan sebelumnya oleh Eskandari, H. World Academy of Science, Engineering and Technology 44, 196-199 (2008). Akan tetapi disini akan dibuktikan orde kekonvergenan dari metode yang belum dilakukan oleh Eskandari. Perbandingan komputasi dari beberapa metode yang dibahas akan diberikan dengan memperhatikan jumlah iterasi, dan COC (Computational Order of Convergence) atau perhitungan orde konvergensi secara komputasi.Item METODE SIMPSON-LIKE TERKOREKSI(2014-03-25) Suryani, Ilis; Imran, M.; Karma, AsmaraThis 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 polynomialItem METODE TRANSFORMASI ELZAKI DALAM MENYELESAIKAN PERSAMAAN DIFERENSIAL BIASA LINEAR ORDE DUA DENGAN KOEFISIEN VARIABEL(2013-06-17) Haryandi, Marpipon; Karma, Asmara; M, MusrainiThis paper discusses how to solve second order linear ordinary differential equations with variable coefficients using ELzaki’s transformation method, Euler’s method and the method of variation of parameters. Then described the ELzaki’s transformation properties to be used in solving second order linear ordinary differential equation with variable coefficients. From this review, ELzaki’s transformation method pro- duces particular solutions of second order linear ordinary differential equations with variable coefficients. While the Euler’s method and the method of variation of parameters only generate the general solution of second order linear ordinary differ-ential equations with variable coefficients.Item PENGGUNAAN METODE DEKOMPOSISI ADOMIAN UNTUK MENYELESAIKAN PERMASALAHAN PADA KALKULUS VARIASI(2016-04-27) Lisnan, Febrian; Karma, AsmaraThis article discusses the use of Adomian decomposition method to solve a variational problem in calculus of variation with known boundary conditions. Process begins by changing the variational problem into Euler-Lagrange equation, and then Adomian decomposition method is applied to the Euler-Lagrange equation. The obtained solution with this method is in a form of convergent power series. Comparison between the solutions obtained by Adomian decomposition method and the exact solution show the efficiency of the Adomian decomposition method.Item Perbaikan Proses Pembelajaran Mata Kuliah Kalkulus Peubah Banyak Di Jurusan Matematika(2015-07-04) M. Natsir; Karma, AsmaraDalam pelaksanaan pcrbaikan proses pembclajaran mata kuliah Kalkulus Peubah Banyak pada Jurusan Matematika FMIPA Universitas Riau dengan beberapa metode antara lain ccramah, diskusi dan tanya javvab yang materinya disesuaikan dengan Garis-garis Besar Program Pengajaran (CJBPP) serta dirinci dalam Satuan Acara Perkuliahan (SAP) berdasarkan silabus dan kurikulum jurusan Matematika FMIPA UNRI, diperoleh peningkatan mutu dan hasil belajar yang cukup signifikan, baik dari segi kehadiran dan keaktifan kuliah mahasiswa maupun dari hasil evaluasi akhir terhadap mata kuliah Kalkulus Peubah Banyak. Dari hasil evaluasi akhir yang telah dilaksanakan diperoleh data : - Rata-rata kehadiran jumlah mahasiswa dengan jumlah 51 orang adalah 96,23%. - Rata-rata IP mata kuliah Kalkulus Peubah Banyak 2,90 yang sebelumnya (th 00/01) hanya 2,81 sehingga terdapat peningkatan IP matakuliah Kalkulus Peubah Banyak sebesar 3,27% Sedangkan prosentase kenaikan berdasarkan kategori nilai Dari tahun sebelumnya (00/01) ketahun (01/02) adalah Nilai A dari 16,6% meningkat menjadi 9,86% Nilai B dari 60,4% meningkat menjadi 68,58% Nilai C dari 22,9% meningkat menjadi 21,56%Item SEBUAH VARIASI BARU METODE NEWTON BERDASARKAN TRAPESIUM KOMPOSIT(2016-04-27) Harahap, Vera Alvionita; Karma, AsmaraThis article discusses the modi cation of Newton's method using the composite trapezoidal rule to approximate an inde nite integral in its derivation. It is analyti- cally demonstrated that the order of convergence of Newton's composite trapezoidal rule is three. Furthermore, computational tests show that the discussed method can be used as an alternative method in their class in solving nonlinear equations.Item SOLUSI SISTEM PERSAMAAN DIFERENSIAL PARSIAL DENGAN MENGGUNAKAN METODE PERTURBASI HOMOTOPI DAN METODE DEKOMPOSISI ADOMIAN(2016-02-04) Rahmadayani, Ita; Syamsudhuha; Karma, AsmaraThis article discusses the solutions of systems of partial differential equations using the homotopy perturbation method and Adomian decomposition method. A numerical example shows that the solution of the partial differential equation obtained by the homotopy perturbation method is better than those of Adomian decomposition method in terms of the speed to approach the exact solution.Item SOLUSI SISTEM PERSAMAAN INTEGRAL VOLTERRA LINEAR DENGAN MENGGUNAKAN METODE MATRIKS EULER(2016-02-04) Sitanggang, Marison Faisal; Karma, AsmaraThis article discusses the solution of system of linear Volterra integral equations in the form of series in Euler polynomials with certain coefficient. The process begins by transforming the system of linear Volterra integral equations to form a matrix equation. Then using some transformation, a system of equations is obtained, whose solution is the coefficients of Euler polynomial series. By substituting the obtained coefficients to the series solution, solutions of linear systems of Volterra integral equations are obtained Furthermore the computational test shows that the solution obtained by the propose method is almost equal to the exact known solutionItem Some Thought on Numerical Integration Based on Interpolation(2017-11-14) Muhammad, Imran; Karma, AsmaraWe discuss and do some analysis on numerical integration based on interpolation, midpoint, trapezoidal rule and Simpson rule. We end up with some new formulas, which are not mentioned in numerical analysis textbooks. The strategy we discuss, in terms of pedagogy, illuminate how research on mathematics can be carry out.Item TEKNIK BARU MENYELESAIKAN SISTEM PERSAMAAN DIFERENSIAL LINEAR ORDE SATU NONHOMOGEN(2014-03-25) Hendri, Yon; Karma, Asmara; MusrainiThis paper discusses a tecnique to solve a system of first order nonhomogeneous linear differential equations with constants-coefficient by writing it in a matrix form. Then order nonhomogeneous linear differential equations are formed which have coefficients involving matrix coefficient that have been formed and solved using variation of parameter method, hance the general solution is obtained from the differential equations discussed. This solution is focused only for andItem THIRD ORDER DERIVATIVE FREE ITERATIVE METHOD(2014-04-12) Imran, Muhammad; Putra, Supriadi; Karma, Asmara; AgusniWe propose a modification of Ujevic method for solving a nonlinear equation by introducing two parameters, after aproximating the derivative by a central difference method. We show that the proposed method is of order three. Numerical experiments are in agreement with analytic results. Using some test functions we compare the proposed method with some discussed methodsItem TWO STEP METHOD WITHOUT EMPLOYING DERIVATIVES FOR SOLVING A NONLINEAR EQUATION(2014-04-12) Imran, Muhammad; Agusni; Karma, Asmara; Putra, SupriadiWe discuss an iterative method for finding root of a nonlinear equation employing central differences to avoid derivatives in the method. We show that this two step method is of order three. Numerical simulations show that the method is comparable with others third order methods