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Using the Haar wavelets to expand the input signal and the output signal, then using the generalized Haar wavelet operational matrix of integration, we present a method to solve numerically the fractional Riccati differential equations. The results of the comparison with other methods indicate that the proposed method is simple and feasible.
An operational matrix of integration based on the linear Legendre multi-wavelets is established, and the procedure for applying the matrix to solve differential equation of a beam on elastic foundation problem which satisfies two-point boundary conditions is formulated. The fundamental idea of the linear Legendre multi-wavelets method is to convert the differential equation into a matrix equation...
In this paper, an operational matrix of integration based on Haar wavelets is introduced, and a procedure for applying the matrix to solve biharmonic equations is formulated. The technique can be used for solving boundary value problems of one-dimensional biharmonic equations. The efficiency of the proposed method is tested with the aid of an example.
Based on analyzing the properties of Legendre wavelets, the extended Legendre wavelets, defined on interval (-r, r), is achieved and its properties are considered. According to the translation property of Legendre wavelets, another method for computing operational matrix of integration P is presented through integrating on subintervals. Furthermore a numerical example for solving linear differential...
This paper establishes a clear procedure for finite-length beam problem and convection-diffusion equation solution via Haar wavelet technique. An operational matrix of integration based on the Haar wavelet is established,and the procedure for applying the matrix to solve the differential equations is formulated. The fundamental idea of Haar wavelet method is to convert the differential equations into...
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