Chebyshev wavelets approach for nonlinear systems of Volterra integral equations

Legendre Wavelets Method for Solving Fractional Population Growth Model in a Closed System

“…Next, we derive the Legendre wavelets operational matrix of fractional integration. By considering (26) and using (28), and (29)…”

“…The main advantages of using an orthogonal basis is that the problem under consideration reduces to a system of linear or nonlinear algebraic system equations [18]; thus this act not only simplifies the problem enormously but also speeds up the computation work during the implementation. This work can be done by truncating the series expansion in orthogonal basis function for the unknown solution of the problem and using the operational matrices [29]. There are two main approaches for numerical solution of fractional differential equations.…”

Solving hybrid fuzzy differential equations by Chebyshev wavelet

“…The fact is that, the proposed scheme transforms a hybrid fuzzy differential equation to a system of algebraic equations using two operational matrices, the first one is the operational matrix of integration presented in [9,11] and the second one is the operational matrix of derivative presented in [25]. It should be noted that both Chebyshev wavelets of the first kind and of the second kind have been attracted considerable attention in solving many different types of differential equations, boundary differential equations, integral equations and fractional integro-differential equations [3,8,9,25].…”

Numerical Solution of Unsteady Flow Between Parallel Plates Using Haar Wavelet-Quasilinearization Method

“…Several researchers [9,10,11,12,13] have contributed to the present growth of mathematical analysis of different types of wavelets. In particular, Chen and Hasio [14] proposed the Haar wavelet which is mathematically the simplest among all the wavelet families.…”