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

Shiralashetti, S.C.; Deshi, A.B.

doi:10.18052/www.scipress.com/BMSA.17.46

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

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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.

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 17)

Pages:

46-56

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.17.46

Citation:

S.C. Shiralashetti and A.B. Deshi, "Haar Wavelet Collocation Method for Solving Riccati and Fractional Riccati Differential Equations", Bulletin of Mathematical Sciences and Applications, Vol. 17, pp. 46-56, 2016

Online since:

November 2016

Authors:

S.C. Shiralashetti, A.B. Deshi

Keywords:

Fractional Riccati Differential Equations, Haar Wavelet Collocation Method, Operational Matrix, Resolution Level, Riccati Differential Equations

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Open Access

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Creative Commons Attribution 4.0 International License

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Cited By:

[1] S. Shiralashetti, R. Mundewadi, "Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method", Bulletin of Mathematical Sciences and Applications, Vol. 18, p. 50, 2017

DOI: https://doi.org/10.18052/www.scipress.com/BMSA.18.50

[2] S. Shiralashetti, H. Ramane, R. Mundewadi, R. Jummannaver, "A Comparative Study on Haar Wavelet and Hosaya Polynomial for the numerical solution of Fredholm integral equations", Applied Mathematics and Nonlinear Sciences, Vol. 3, p. 447, 2018