On the accuracy of the Haar wavelet discretization method

Majak, Jüri; Shvartsman, B.S.; Karjust, Kristo; Mikola, M.; Haavajõe, Anti; Pohlak, M.

doi:10.1016/j.compositesb.2015.06.008

Cited by 81 publications

(39 citation statements)

References 39 publications

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“…The results show that the proposed technique is efficient and accurate. Some analytical method by using HW can be found in the references [40,41]. The performance of the method is equally suitable for these equations.…”

Section: Discussionmentioning

confidence: 99%

A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

2019

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In this paper, a new collocation method based on Haar wavelet is developed for numerical solution of Riccati type differential equations with non-integer order. The fractional derivatives are considered in the Caputo sense. The method is applied to one test problem. The maximum absolute estimated error functions are calculated, and the performance of the process is demonstrated by calculating the maximum absolute estimated error functions for a distinct number of nodal points. The results show that the method is applicable and efficient.

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Section: Discussionmentioning

confidence: 99%

A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

2019

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“…Matlab R2017a has been used for the simulations. We have also calculated the order of convergence, which is expressed as [40,41]…”

Section: Numerical Examplesmentioning

confidence: 99%

Solution of Fractional Order Riccati Differential Equations Using Euler Wavelet Method

Ocak

2018

Scientia Iranica

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The Fractional-order Di erential Equations (FDEs) have the ability to model the real-life phenomena better in a variety of applied mathematics, engineering disciplines including di usive transport, electrical networks, electromagnetic theory, probability, and so forth. In most cases, there are no analytical solutions; therefore, a variety of numerical methods have been developed for obtaining solutions to the FDEs. In this paper, we derive numerical solutions to various fractional-order Riccati-type di erential equations using the Euler Wavelet Method (EWM). The Euler wavelet operational matrix method converts the fractional di erential equations to a system of algebraic equations. Illustrative examples are included to demonstrate validity and e ciency of the technique.

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“…Then we need to find the upper bound of a 11 . By applying the orthogonal property (55) in (53) and setting i, i = 1, we see that…”

Section: Definition 2 According Tomentioning

confidence: 99%

“…Siraj-ul-Islam et al 8,9 proved the convergence of the Haar wavelet series. Majak et al 10,11 published a convergence theorem for solving ODEs using the wavelet method 1,2 . To the best of our knowledge, the convergence analysis of a wavelet-based method for solving PDEs has not been presented before.…”

Section: Introductionmentioning

confidence: 99%

A convergence analysis of the numerical solution of boundary-value problems by using two-dimensional Haar wavelets

Wichailukkana¹,

Novaprateep²,

Boonyasiriwat³

2016

ScienceAsia

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On the accuracy of the Haar wavelet discretization method

Cited by 81 publications

References 39 publications

A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

A New Algorithm for Fractional Riccati Type Differential Equations by Using Haar Wavelet

Solution of Fractional Order Riccati Differential Equations Using Euler Wavelet Method

A convergence analysis of the numerical solution of boundary-value problems by using two-dimensional Haar wavelets

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