A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals

An operational matrix method for solving linear Fredholm--Volterra integro-differential equations

“…In our case, we use an integration matrix instead. Numerical results show that the accuracy of our method is superior to that of the homotopy perturbation method [33], Bernoulli polynomials [5], Tau method [22] and the Bessel collocation method [34] with collocation points. Our method yields good approximations of the solutions of the considered problems even for small values of N .…”

“…As for the CAS wavelet method [8] and differential transform method [9], although the errors of the present method are smaller, the related papers do not include any parameter values in order to present a fair comparison. In addition, Table 3 compares the errors of our solutions with N = 10 with those obtained by Bernoulli polynomials [5] with the same N value. The values demonstrate that errors of the present method are smaller for this N value.…”

A new spectral method for a class of linear boundary value problems

“…In [16] the authors applied Galerkin weighted residual method using Bernoulli polynomials as trial functions for approximating the solutions of second order boundary value problems. The advantage of the use of Bernoulli polynomials over different polynomial basis for approximating an arbitrary unknown function has been highlighted (see for example [4,27]). …”

Genocchi Wavelet-like Operational Matrix and its Application for Solving Non-linear Fractional Differential Equations

“…In this paper, we present a wavelet-like basis based on an important member of Appell polynomials called Genoc-chi polynomial, though the polynomials are not besed on orthogonal functions, they share some advantageous properties with the polynomials in the Appell family, such as Bernoulli polynomials, over other classical orthogonal polynomials when approximating an arbitrary function. These advantages are stated in [20].…”