Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration

Department of Mathematics, Islamic Azad University (Central Tehran Branch) Tehran, Iran
Applied Mathematics and Computation (Impact Factor: 1.55). 05/2007; 188(1):417-426. DOI: 10.1016/j.amc.2006.10.008
Source: DBLP


In this paper we present operational matrix of integration (OMI) of Chebyshev wavelets basis and the product operation matrix (POM) of it. Some comparative examples are included to demonstrate the superiority of operational matrix of Chebyshev wavelets to those of Legendre wavelets.

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    • "Eventually, to calculate integration of f(í µí±¥), the product matrix of integration (P) is operated on right side of equation (1) [6] [7] [8] [9] [10] [11]. "
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    ABSTRACT: This paper presents an optimum measurement for the dynamic responses of structures from the operation of integration to respective derivation of acceleration's data using free-scaled wavelet functions. For this purpose, the numerical approach of integration and derivation has been developed for displacement measurement or determination of the third-order derivative (known as quantity of the jerk) from acquired accelerations. A simple improved algorithm is developed in order to optimally measure the dynamic quantities particularly, using Chebyshev and Haar wavelet functions. It is deduced that, stable measurement of dynamic quantities is independently achieved from the structural materials through a satisfactory optimum algorithm; that is capable of online monitoring, while emphasizing on maximum accuracy of the measurement with less computational time.
    Journal of Physics Conference Series 07/2015; 628(1). DOI:10.1088/1742-6596/628/1/012024
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    • "Legendre wavelets have been previously employed for solving various differential and integral equations (see for example, [35,34,36,46–48]). Also, first and second kinds Chebyshev wavelets have been used for solving some integer and fractional orders differential equations (see for example, [7] [56] [31] [25]). Recently, Abd-Elhameed et al. in [2] [3], have introduced new Chebyshev wavelets algorithms for solving second-order boundary value problems. "
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    ABSTRACT: In this paper, a new spectral algorithm based on employing ultraspherical wavelets along with the spectral collocation method is developed. The proposed algorithm is utilized to solve linear and nonlinear even-order initial and boundary value problems. This algorithm is supported by studying the convergence analysis of the used ultraspherical wavelets expansion. The principle idea for obtaining the proposed spectral numerical solutions for the above-mentioned problems is actually based on using wavelets collocation method to reduce the linear or nonlinear differential equations with their initial or boundary conditions into systems of linear or nonlinear algebraic equations in the unknown expansion coefficients. Some specific important problems such as Lane–Emden and Burger's type equations can be solved efficiently with the suggested algorithm. Some numerical examples are given for the sake of testing the efficiency and the applicability of the proposed algorithm.
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    • "Heydari et al. [39] established the CWM for telegraph type partial differential equations with boundary conditions. Babolian and Fattahzadeh [40] had established the Chebyshev wavelet operational matrix of integration for solving the differential equations. Ghasemi and Tavassoli Kajani [41] had introduced the CWM for solving the time-varying delay systems. "
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    ABSTRACT: In this paper, mathematical modeling of porous catalysts is discussed. An efficient wavelet method, called the shifted second kind Chebyshev wavelet method is used to obtain the solution for the concentration of species. An approximate polynomial expression for concentration and the effectiveness factors are obtained for general nonlinear Langmiur–Hinshelwood–Haugen–Watson type models which have variety of real rate function. To the best of our knowledge until there is no rigorous wavelet solution has been addressed in this model. The power of the manageable method is confirmed. The concentration and the effectiveness factors are also computed for the various limiting cases of LHHW models.
    MATCH Communications in Mathematical and in Computer Chemistry 06/2015; 73(3):705-727. · 1.47 Impact Factor
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