A piecewise variational iteration method for Riccati differential equations

Geng, Fazhan; Yang, Lin; Cui, Minggen

doi:10.1016/j.camwa.2009.03.063

Cited by 63 publications

(58 citation statements)

References 22 publications

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“…The main advantage of this method is its simplicity and less computation costs: it is due to the sparcity of the transform matrices and to the small number of significant wavelet coefficients. We have achieved a very good agreement between the approximate solution obtained by existing methods [24,13,20]. The results show that HWCM is reliable and efficient method for solving these problems.…”

Section: Discussionsupporting

confidence: 60%

“…In addition, Abbasbandy [1] presented Homotopy perturbation method (HPM) for determining the solution of Riccati equations and the compared accuracy of the obtained solution with that derived by ADM. A novel and effective method for determining the approximate solution of these equations with constant and varying coefficients proposed in [24]. In [13] Modified variational iteration method (MVIM) presented to obtain a highly accurate numerical solution of Riccati equations.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we establish a clear procedure for solving the proposed equations via HWCM; comparisons are made between HWCM and existing methods [13,20,24] with the exact solutions. The results reveal that the proposed method is very effective and simple and can be applied to other nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

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Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations

Shiralashetti

Deshi

2016

BMSA

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Abstract. In this paper, numerical solutions of Riccati and fractional Riccati differential equations are obtained by the Haar wavelet collocation method. An operational matrix of integration based on the Haar wavelet is established, and the procedure for applying the matrix to solve these equations. The fundamental idea of Haar wavelet method is to convert the proposed differential equations into a group of non-linear algebraic equations. The accuracy of approximate solution can be further improved by increasing the level of resolution and an error analysis is computed. The examples are given to demonstrate the fast and flexibility of the method. The results obtained are in good agreement with the exact in comparison with existing ones and it is shown that the technique introduced here is robust, easy to apply and is not only enough accurate but also quite stable.

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Section: Discussionsupporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

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Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations

Shiralashetti

Deshi

2016

BMSA

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“…For most cases, one must make use of numerical techniques or approximate approaches for the obtainment of solutions. This is why the problem has attracted quite a bit of attention in the recent past and has been the topic of study of many authors [4,5,6] [4,9]. The Taylor, Chebyshev and Legendre (matrix and collocation) methods have been employed by Sezer et al [10], and Akyuz [11] to solve the famous Riccati equations.…”

Section: Introductionmentioning

confidence: 99%

An Effective Perturbation Iteration Algorithm for Solving Riccati Differential Equations

Khalid¹,

Sultana²,

Zaidi³

et al. 2015

IJCA

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In the following study, a novel approach called the Perturbation Iteration Algorithm P IA has been proposed and subsequently adopted for deriving and solving the Riccati differential equation. This new Perturbation Iteration Method is efficient and has no requirement of a small parameter assumption as its earlier classical counterparts do. Some examples have been presented to exhibit how simply and efficiently the proposed method works. After deriving the exact solution of the Riccati equation, the capability and the simplicity of the proposed technique is clarified. A percentage error for each example has also been presented.

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“…To improve the convergence speed and enlarge the interval of convergence for VIM series solutions, a number of modifications were propounded [37][38][39]. There are many modifications of VIM, exclusively appropriate for fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains

2017

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Abstract:In this paper, we introduced a new generalization method to solve fractional convection-diffusion equations based on the well-known variational iteration method (VIM) improved by an auxiliary parameter. The suggested method was highly effective in controlling the convergence region of the approximate solution. By solving some fractional convection-diffusion equations with a propounded method and comparing it with standard VIM, it was concluded that complete reliability, efficiency, and accuracy of this method are guaranteed. Additionally, we studied and investigated the convergence of the proposed method, namely the VIM with an auxiliary parameter. We also offered the optimal choice of the auxiliary parameter in the proposed method. It was noticed that the approach could be applied to other models of physics.

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A piecewise variational iteration method for Riccati differential equations

Cited by 63 publications

References 22 publications

Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations

Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations

An Effective Perturbation Iteration Algorithm for Solving Riccati Differential Equations

A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains

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