# American Institute of Mathematical Sciences

• Previous Article
Spectral Jacobi-Galerkin methods and iterated methods for Fredholm integral equations of the second kind with weakly singular kernel
• DCDS-S Home
• This Issue
• Next Article
Couette flows of a viscous fluid with slip effects and non-integer order derivative without singular kernel
June  2019, 12(3): 665-684. doi: 10.3934/dcdss.2019042

## Comparative study of a cubic autocatalytic reaction via different analysis methods

 a. Department of Mathematics, College of Arts and Sciences, Najran University, 61441, Najran, Saudi Arabia b. Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen

* Corresponding author: khaledma_sd@hotmail.com

Received  June 2017 Revised  September 2017 Published  September 2018

In this paper we discuss an approximate solutions of the space-time fractional cubic autocatalytic chemical system (STFCACS) equations. The main objective is to find and compare approximate solutions of these equations found using Optimal q-Homotopy Analysis Method (Oq-HAM), Homotopy Analysis Transform Method (HATM), Varitional Iteration Method (VIM) and Adomian Decomposition Method (ADM).

Citation: Khaled Mohammed Saad, Eman Hussain Faissal AL-Sharif. Comparative study of a cubic autocatalytic reaction via different analysis methods. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 665-684. doi: 10.3934/dcdss.2019042
##### References:

show all references

##### References:
The absolute error between the 3-terms of Oq-HAM solutions and numerical method using Mathematica for (4)-(5) with $\alpha = 1, \beta = 1, a = 0.001, b = 0.001, h = -3.055, n = 5$
The absolute error between the 3-terms of HATM solutions and numerical method using Mathematica for (4)-(5) with $\alpha = 1, \beta = 1, a = 0.001, b = 0.001, h = -0.64$
The absolute error between the second approximation by VIM and the numerical method using Mathematica for (4)-(5) with $\alpha = 1, \beta = 1, a = 0.001, b = 0.001 .$
The absolute error between the 3-terms of ADM and the numerical method using Mathematica for (4)-(5) with $\alpha = 1, \beta = 1, a = 0.001, b = 0.001$
The absolute error between the 3-terms of Oq-HAM solutions and numerical method using Mathematica for (4)-(5) with $\alpha = 0.9, \beta = 0.99, a = 0.001, b = 0.001, h = -1.9, n = 5$
The absolute error between the 3-terms of HATM solutions and numerical method using Mathematica for (4)-(5) with $\alpha = 0.9,\beta = 0.99, a = 0.001, b = 0.001, h = -0.64$
The absolute error between the second approximation by VIM and the numerical method using Mathematica for (4)-(5) with $\alpha = 0.9, \beta = 0.99, a = 0.001, b = 0.001$
The absolute error between the 3-terms of ADM and the numerical method using Mathematica for (4)-(5) with $\alpha = 0.9, \beta = 0.99, a = 0.001, b = 0.001$
The comparison of Oq-HAM, HATM, VIM and ADM for (4)-(5) with numerical method in Mathematica for $x = 0.1, 5, 20, 40,100$ respectively and $\alpha = 1, \beta = 1, a = 0.001, b = 0.001, n = 5, h_{Oq-HAM} = -3.055, h_{HATM} = 0.64.$ Dash - dotted line (Oq-HAM), dotted line (HATM), dash line (VIM), and solid line (ADM)
The comparison of Oq-HAM, HATM, VIM and ADM for (4)-(5) with numerical method in Mathematica for $x = 0.1, 5, 20, 40,100$ respectively and $\alpha = 1, \beta = 1, a = 0.001, b = 0.001, n = 5, h_{Oq-HAM} = -3.055, h_{HATM} = 0.64.$ Dash - dotted line (Oq-HAM), dotted line (HATM), dash line (VIM), and solid line (ADM)
The plot of Oq-HAM, HATM, VIM and ADM for (4)-(5) with $\alpha = 0.4,\beta = 0.7, a = 0.4, b = 0.2, n = 5, h_{Oq-HAM} = -3.00, h_{HATM} = -0.64 .$ Dash - dotted line (Oq-HAM), dotted line (HATM), dash line (VIM), and solid line (ADM)
The plot of Oq-HAM, HATM, VIM and ADM for (4)-(5) with $\alpha = 0.7,\beta = 0.9, a = 0.4, b = 0.2, n = 5, h_{Oq-HAM} = -3.00, h_{HATM} = -0.64 .$ Dash - dotted line (Oq-HAM), dotted line (HATM), dash line (VIM), and solid line (ADM)
The plot of Oq-HAM, HATM, VIM and ADM for (4)-(5) with $\alpha = 0.99,\beta = 0.99, a = 0.4, b = 0.2, n = 5, h_{q-HAM} = -3.00, h_{HATM} = -0.64 .$ Dash - dotted line (Oq-HAM), dotted line (HATM), dash line (VIM), and solid line (ADM)
The surface of Oq-HAM for (4)-(5) with $\alpha = 0.5, 0.8, 1.00,\beta = 0.75,0.90, 1.00$ and $a = 0.4, b = 0.2, n = 5, h_{Oq-HAM} = -3.00$
The surface of HATM for (4)-(5) with $\alpha = 0.5, 0.8, 1.00,\beta = 0.75,0.90, 1.00$ and $a = 0.4, b = 0.2, h_{HATM} = -0.64$
The surface of VIM for (4)-(5) with $\alpha = 0.5, 0.8, 1.00,\beta = 0.75,0.90, 1.00$ and $a = 0.4, b = 0.2$
The surface of ADM for (4)-(5) with $\alpha = 0.5, 0.8, 1.00,\beta = 0.75,0.90, 1.00$ and $a = 0.4, b = 0.2$
 [1] Figen Özpinar, Fethi Bin Muhammad Belgacem. The discrete homotopy perturbation Sumudu transform method for solving partial difference equations. Discrete & Continuous Dynamical Systems - S, 2019, 12 (3) : 615-624. doi: 10.3934/dcdss.2019039 [2] Zhengshan Dong, Jianli Chen, Wenxing Zhu. Homotopy method for matrix rank minimization based on the matrix hard thresholding method. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 211-224. doi: 10.3934/naco.2019015 [3] Zhichuan Zhu, Bo Yu, Li Yang. Globally convergent homotopy method for designing piecewise linear deterministic contractual function. Journal of Industrial & Management Optimization, 2014, 10 (3) : 717-741. doi: 10.3934/jimo.2014.10.717 [4] Chunyang Zhang, Shugong Zhang, Qinghuai Liu. Homotopy method for a class of multiobjective optimization problems with equilibrium constraints. Journal of Industrial & Management Optimization, 2017, 13 (1) : 81-92. doi: 10.3934/jimo.2016005 [5] Xiaona Fan, Li Jiang, Mengsi Li. Homotopy method for solving generalized Nash equilibrium problem with equality and inequality constraints. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1795-1807. doi: 10.3934/jimo.2018123 [6] Zhengyong Zhou, Bo Yu. A smoothing homotopy method based on Robinson's normal equation for mixed complementarity problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 977-989. doi: 10.3934/jimo.2011.7.977 [7] Zainidin Eshkuvatov. Homotopy perturbation method and Chebyshev polynomials for solving a class of singular and hypersingular integral equations. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 337-350. doi: 10.3934/naco.2018022 [8] Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2020013 [9] C E Yarman, B Yazıcı. A new exact inversion method for exponential Radon transform using the harmonic analysis of the Euclidean motion group. Inverse Problems & Imaging, 2007, 1 (3) : 457-479. doi: 10.3934/ipi.2007.1.457 [10] Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 [11] Yong Duan, Jian-Guo Liu. Convergence analysis of the vortex blob method for the $b$-equation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1995-2011. doi: 10.3934/dcds.2014.34.1995 [12] Fang Zeng, Pablo Suarez, Jiguang Sun. A decomposition method for an interior inverse scattering problem. Inverse Problems & Imaging, 2013, 7 (1) : 291-303. doi: 10.3934/ipi.2013.7.291 [13] Lijian Jiang, Craig C. Douglas. Analysis of an operator splitting method in 4D-Var. Conference Publications, 2009, 2009 (Special) : 394-403. doi: 10.3934/proc.2009.2009.394 [14] Binjie Li, Xiaoping Xie, Shiquan Zhang. New convergence analysis for assumed stress hybrid quadrilateral finite element method. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2831-2856. doi: 10.3934/dcdsb.2017153 [15] Junjiang Lai, Jianguo Huang. A finite element method for vibration analysis of elastic plate-plate structures. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 387-419. doi: 10.3934/dcdsb.2009.11.387 [16] Roberto Avanzi, Nicolas Thériault. A filtering method for the hyperelliptic curve index calculus and its analysis. Advances in Mathematics of Communications, 2010, 4 (2) : 189-213. doi: 10.3934/amc.2010.4.189 [17] Matthew O. Williams, Clarence W. Rowley, Ioannis G. Kevrekidis. A kernel-based method for data-driven koopman spectral analysis. Journal of Computational Dynamics, 2015, 2 (2) : 247-265. doi: 10.3934/jcd.2015005 [18] Derek H. Justice, H. Joel Trussell, Mette S. Olufsen. Analysis of Blood Flow Velocity and Pressure Signals using the Multipulse Method. Mathematical Biosciences & Engineering, 2006, 3 (2) : 419-440. doi: 10.3934/mbe.2006.3.419 [19] Jia Cai, Junyi Huo. Sparse generalized canonical correlation analysis via linearized Bregman method. Communications on Pure & Applied Analysis, 2020, 19 (8) : 3933-3945. doi: 10.3934/cpaa.2020173 [20] Zhong-Zhi Bai. On convergence of the inner-outer iteration method for computing PageRank. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 855-862. doi: 10.3934/naco.2012.2.855

2018 Impact Factor: 0.545

## Metrics

• HTML views (178)
• Cited by (0)

• on AIMS