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All Journal Matematika: Jurnal Teori dan Terapan Operations Research: International Conference Series
Ira Sumiati
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Mathematics

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Solusi Persamaan Diferensial Fraksional Riccati Menggunakan Adomian Decomposition Method dan Variational Iteration Method Muhamad Deni Johansyah; Herlina Napitupulu; Erwin Harahap; Ira Sumiati; Asep K. Supriatna
Matematika Vol 18, No 1 (2019): Jurnal Matematika
Publisher : Universitas Islam Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jmtm.v18i1.4931

Abstract

Abstrak. Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Paper ini membahas persamaan diferensial fraksional Riccati dengan orde diantara nol dan satu, dan koefisien konstan. Metode numerik yang digunakan untuk mendapatkan solusi dari persamaan diferensial fraksional Riccati adalah Adomian Decomposition Method (ADM) dan Variational Iteration Method (VIM). Tujuan dari paper ini adalah untuk memperluas penerapan ADM dan VIM dalam menyelesaikan persamaan diferensial fraksional Riccati nonlinear dengan turunan Caputo. Perbandingan solusi yang diperoleh menunjukkan bahwa VIM adalah metode yang lebih sederhana untuk mencari solusi persamaan diferensial fraksional Riccati nonlinier dengan orde antara nol dan satu, kemudian hasil yang diperoleh disajikan dalam bentuk grafik.Kata kunci: diferensial, fraksional, riccati, adomian dekomposisiThe solution of Riccati Fractional Differential Equation using Adomian Decomposition methodAbstract. Generally, the order of differential equations is a natural numbers, but this order can be formed into fractional, called as fractional differential equations.  In this paper, the Riccati fractional differential equations with order between zero and one, and constant coefficient is discussed.  The numerical methods used to obtain solutions from Riccati fractional differential equations are the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM).  The aim of this paper is to expand the application of ADM and VIM in solving nonlinear Riccati fractional differential equations with Caputo derivatives.  The comparison of the obtained solutions shows that VIM is simpler method for finding solutions to Riccati nonlinear fractional differential equations with order between zero and one. The obtained results are presented graphically.Keywords: riccati, fractional, differential, adomian, decomposition
Adomian Decomposition Method and The Other Integral Transform Ira Sumiati; Sukono Sukono
Operations Research: International Conference Series Vol 1, No 4 (2020)
Publisher : Indonesian Operations Research Association (IORA)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47194/orics.v1i4.151

Abstract

The Adomian decomposition method is an iterative method that can be used to solve integral, differential, and integrodifferential equations. The differential equations that can be solved by this method can be of integer or fractional order, ordinary or partial, with initial or boundary value problems, with variable or constant coefficients, linear or nonlinear, homogeneous or nonhomogeneous. This method divides the equation into two forms, namely linear and nonlinear, so that it can solve equations without linearization, discretization, perturbation, or other restrictive assumptions. The basic concept of this method assumes that the solution can be decomposed into an infinite series. This method decomposes the nonlinear form (if any) of the equation with the Adomian polynomial series. This decomposition method can be combined with various integral transform, such as Laplace, Sumudu, Elzaki, and Mohand. The main idea of this technique assumes that the solution can be decomposed into an infinite series, then applies the integral transform to the differential equation. The main advantage of this technique is that the solution can be expressed as an infinite series that converges rapidly to the exact solution. This paper aims to combine the Adomian decomposition method with the new integral transform introduced by Kumar et al. (2022). This integral transform is called the Rishi transform. A scheme for solving fractional ordinary differential equations using the combined method is presented in this paper.
Co-Authors Asep K. Supriatna Erwin Harahap Herlina Napitupulu Muhammad Deni Johansyah Sukono Sukono