An efficient numerical approximation for the linear class of Fredholm integro-differential equations based on Cattani’s method

Weak form quadrature solution of 2mth-order Fredholm integro-differential equations

“…(13) with the number of sampling points set to be M . After solving the equations, unknown values of the elements in the set {u(x i ), i = A c c e p t e d M a n u s c r i p t 1, 2, · · · , M } {∂ r x u(±1), r = 1, 2, · · · , m − 1} are obtained, which can be adopted in the generalized differential analog (10) to approximate the derivatives at the sampling points. Hermite interpolations (12) can be used to convert the discrete data into an approximate solution for the problem…”

“…The development of numerical methods for such equations has been rather extensive, such as the finite difference method, the compact finite differential method [3], the differential transform method [4], the Galerkin method [5][6][7], the wavelet-Galerkin method [8], the Haar wavelet method [9], the Shannon wavelet method [10], the sinecosine wavelet method [11], the CAS wavelet method [12], the trigonometric wavelets method [13], the Legendre wavelets method [14], the Legendre polynomial method [15][16][17], the Bessel polynomial method [18], the Taylor polynomial method [19][20][21][22][23], the Chebyshev collocation method [24], the B-Spline collocation method [25], the Hermite collocation method [26], the variational iteration method [17,[27][28][29], the Clenshaw Curtis quadrature formulae [30], the Monte Carlo method [31], the Tau method [32], the homotopy perturbation method [11,33], the reproducing kernel Hilbert space method [34], the pseudospectral method [35], the meshless method [36], the operational approach with Pade approximant [37], the Adomian decomposition method [38], and so forth.…”

On the approximate solution of integro-differential equations arising in oscillating magnetic fields

“…First, we recall the definitions and the notation of the Shannon wavelets family from [11]. The starting point for the definition of the Shannon wavelets family is the Sinc or Shannon scaling function.…”

“…Our discussion is based on the connection coefficients of the Shannon wavelets which were proposed by Cattani in [6]. Detailed description and analysis of this technique may be found in [6], [7], [11] and references therein.…”

Computational methods of solving the boundary value problems for the loaded differential and Fredholm integro‐differential equations

“…Integro-differential equations are often encountered in applications being the mathematical models for various processes occurring in natural sciences. Qualitative properties of different problems for integro-differential equations and methods for solving these problems are studied in the works of many authors (see, eg, previous studies [1][2][3][4][5][6][7][8][9] and references cited therein).…”