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A Coiflets-Based Wavelet Laplace Method for Solving the Riccati Differential Equations

Xiaomin Wang
2014 Journal of Applied Mathematics  
With the help of Laplace transform, the fractional differential equation was converted into equivalent integral equation of convolution type.  ...  A wavelet iterative method based on a numerical integration by using the Coiflets orthogonal wavelets for a nonlinear fractional differential equation is proposed.  ...  Acknowledgments This work was supported by National Natural Science Foundation of China (11302081) and Huazhong Agricultural University Scientific and Technological Self-innovation Foundation under Grant  ... 
doi:10.1155/2014/257049 fatcat:d6vvrhcn6rew5po4dczgx4gkaa

A New Iterative Method for Riccati Differential Equation

Shivaji Tate
2017 International Journal for Research in Applied Science and Engineering Technology  
Riccati differential equations are usually arises in many fields of applied science.  ...  In this paper, we suggest a new iterative method proposed by Daftardar-Gejji and Jafari to solve the Riccati differential equation. We use software Mathematic for computations.  ...  The book of Reid [8] contains the fundamental theories of Riccati equation, with applications to random processes, optimal control, and diffusion problems.  ... 
doi:10.22214/ijraset.2017.11375 fatcat:maprpba3jfgejjzpflaxniwiua

Application of variational iteration method to a general Riccati equation

B. Batiha, M. S. M. Noorani, I. Hashim
2007 International Mathematical Forum  
In this paper, the variational iteration method (VIM) is applied to the solution of general Riccati differential equations.  ...  Comparisons with exact solution and the fourth-order Runge-Kutta method show that the VIM is a powerful method for the solution of nonlinear equations.  ...  Acknowledgement The financial support received from the Academy of Sciences Malaysia under the SAGA grant no. P24c is gratefully acknowledged.  ... 
doi:10.12988/imf.2007.07248 fatcat:gc5mpc4bgvcx5lxn3n7b7oklwi

Application of Generalized Differential Transform Method to Special Cases of Riccati Differential Equation of Fractional Order

2019 International journal of recent technology and engineering  
Accuracy and competence of the proposed method is verified through numerical solution of some special cases of Riccati Differential equation of fractional order.  ...  In this paper, we acquire the inexact solutions of Special cases of Riccati Differential equation of Fractional order using Generalized Differential Transform Method (GDTM).  ...  DTM is used to find the solution of different kinds of Riccati differential equation such solution of first order , second order and system of Riccati equations [1] , Differential Transform Method for  ... 
doi:10.35940/ijrte.c4939.098319 fatcat:nchunnre2vazfpfca6n3kblgs4

Solving of Some Random Partial Differential Equations by Using Differential Transformation Method and Laplace- Padé Method

Halil ANAÇ, Mehmet MERDAN, Zafer BEKİRYAZICI, Tülay KESEMEN
2019 Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi  
Functions for the expected values and the variances of the approximate analytical solutions of the random equations are obtained.  ...  A few examples are given to illustrate the efficiency of the solutions obtained with the random Differential Transformation Method (rDTM).  ...  They found an analytical mean-fourth convergent series solution to a nonlinear random Riccati differential equation with the random DTM.  ... 
doi:10.17714/gumusfenbil.404332 fatcat:krp5shqqlvdvnaoqbqjg6udie4

New Implementation of Residual Power Series for Solving Fuzzy Fractional Riccati Equation

Moath Ali Alshorman, Nurnadiah Zamri, Mohammed Ali, Asia Khalaf Albzeirat
2018 Journal of Modeling and Optimization  
An analytical solution of fuzzy fractional riccati equation is obtained as a convergent fractional power series.  ...  This paper reveals a computational method using a Residual Power Series Method (RPSM) for the solution of fuzzy fractional riccati equation under caputo fractional differentiability.  ...  Currently, in light of the growing fractional concept for the order of differential equation, fractional riccati equation has appeared as a more comprehensive form with a different value of derivative  ... 
doi:10.32732/jmo.2018.10.2.81 fatcat:jf2473b2xzd3povpbbeyqlh7te

Solution of matrix Riccati differential equation for nonlinear singular system using neural networks

J. Abdul Samath, N. Selvaraju
2010 International Journal of Computer Applications  
In this paper, the solution of the matrix Riccati differential equation(MRDE) for nonlinear singular system is obtained using neural networks.  ...  The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the MRDE obtained from well known traditional Runge Kutta(RK)method and nontraditional neural network method  ...  A variety of numerical algorithms have been developed for solving the algebraic Riccati equation.  ... 
doi:10.5120/575-181 fatcat:yv4tahm23vgfpgkzu25evaijyi

An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations

M. M. Khader, A. M. S. Mahdy, M. M. Shehata
2014 Applied Mathematics  
We implement these formulae to solve numerically Riccati, Logistic and delay differential equations with variable coefficients.  ...  The book of Reid [14] contains the fundamental theories of Riccati equation, with applications to random processes, optimal control, and diffusion problems.  ...  We implement these formulae to solve numerically Riccati, Logistic and delay differential equations.  ... 
doi:10.4236/am.2014.515228 fatcat:sd6isfmzf5a75pwsitksxbalaq

Homotopy Perturbation Method for Solving Generalized Riccati Differential Equation

Mohammed S. Mechee, Ghassan A. Al-Juaifri
2019 Al-Nahrain Journal of Science  
In this work, we have studied a class of nonlinear Riccati differential equation which is used as mathematical models in many physically significant fields and applied science.  ...  The approximated solutions are agreed well with analytical solutions for the tested problems.  ...  The authors would like to thank university of Kufa for supporting this research project  ... 
doi:10.22401/anjs.00.2.13 fatcat:u32mzapymbbq5pg6we2hgcepy4

Solving Riccati time-dependent models with random quadratic coefficients

J.-C. Cortés, L. Jódar, R. Company, L. Villafuerte
2011 Applied Mathematics Letters  
This paper deals with the construction of approximate solutions of a random logistic differential equation whose nonlinear coefficient is assumed to be an analytic stochastic process and the initial condition  ...  Applying p-mean stochastic calculus, the nonlinear equation is transformed into a random linear equation whose coefficients keep analyticity.  ...  Acknowledgments This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universitat Politècnica de València grant PAID06-09-2588 and Mexican Conacyt.  ... 
doi:10.1016/j.aml.2011.06.024 fatcat:p7gmylrw65g6di6cwb2fdnbrhy

A random differential transform method: Theory and applications

L. Villafuerte, B.M. Chen-Charpentier
2012 Applied Mathematics Letters  
An analytical mean fourth convergent series solution is found for a nonlinear random Riccati differential equation by using the random DTM.  ...  Besides obtaining the series solution of the Riccati equation, we provide approximations of the main statistical functions of the stochastic solution process such as the mean and variance.  ...  To illustrate the power of this method of solution, a Riccati differential equation with randomness in the initial condition and in the coefficients is chosen.  ... 
doi:10.1016/j.aml.2011.12.033 fatcat:yo5j6rutkvaqdknn7amfatgkli

Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains

Jafar Biazar, Mohsen Didgar
2015 International Journal of Differential Equations  
We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.  ...  decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations  ...  Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper. 6 International Journal of Differential Equations  ... 
doi:10.1155/2015/580741 fatcat:ziwjlgd35raodirn7tvafwszyu

Transfer Relations for Electromagnetic Wave Scattering From Periodic Dielectric One-Dimensional Interface: Te Polarization

Yu. N. Barabanenkov, V.L. Kouznetsov, M. Yu. Barabanenkov
1999 Journal Electromagnetic Waves and Applications  
ACKNOWLEDGMENT The research described in this publication was made possible in part by grant from the Russian Foundation for Basic Research numbers 98-02-17086 and 99-02-17864.  ...  NUMERICAL SOLUTION TO THE MATRIX RICCATI EQUATION The matrix Riccati equation (83) is an infinite system of differential equations.  ...  Results of Numerical Solution to The Matrix Riccati Equation Some results of numerical solution to the truncated matrix Riccati equation (83) are plotted in Figs. 3-6.  ... 
doi:10.1163/156939399x00664 fatcat:5mamiyqsdvbg7dckxlfsocpyhm

Some notes to extend the study on random non-autonomous second order linear differential equations appearing in Mathematical Modeling [article]

J. Calatayud and J.-C. Cortés and M. Jornet
2018 arXiv   pre-print
Another novelty is that we tackle the non-homogeneous equation with a theorem of existence of mean square analytic solution and a numerical example.  ...  Villafuerte, Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties, Advances in Difference Equations, 2018:392, 1--29 (2018)]  ...  Conflict of Interest Statement The authors declare that there is no conflict of interests regarding the publication of this article.  ... 
arXiv:1811.07887v1 fatcat:4cc4sqf2ezh67jajcef6h5ca44

Numerical treatment for solving fractional Riccati differential equation

M.M. Khader
2013 Journal of the Egyptian Mathematical Society  
By this method the given problem is reduced to a problem for solving a system of algebraic equations, and by solving this system, we obtain the solution of FRDE.  ...  This paper presents an accurate numerical method for solving fractional Riccati differential equation (FRDE). The proposed method so called fractional Chebyshev finite difference method (FCheb-FDM).  ...  The book of Reid [16] contains the fundamental theories of Riccati equation, with applications to random processes, optimal control, and diffusion problems.  ... 
doi:10.1016/j.joems.2012.09.005 fatcat:4ngjqcfkbzazbnjebpyzrutzp4
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