A method for the numerical solution of the integro-differential equations

Numerical Solution of Second-Order Fredholm Integrodifferential Equations with Boundary Conditions by Quadrature-Difference Method

“…DiffTrans: differential transformation method, [7]. Tau method: Tau method with piecewise approximate solution of degree 5, [9].…”

“…Therefore, many authors have studied the numerical solutions of Fredholm integrodifferential equations. Several numerical methods were used such as Adomian's Decomposition method [1], Generalised minimal residual method (GMRES) [2], CAS Wavelet method [3], compact finite difference [4], Lagrange interpolation method [5], Spline Collocation [6], differential transformation method [7], variational iteration method [8], Tau method [9], Legendre collocation matrix method [10], and quadrature-difference method [11,12]. LFIDEs are usually difficult to solve analytically.…”

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

“…Errors obtained by our method are smaller than those of the Bessel collocation method [34] and HPM [33] for listed parameter values, which is also shown visually in Figure 1. 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.…”

“…We also obtained the approximate solutions with N = 3, 7, 10. In Table 2, absolute errors of the present method corresponding to N = 3, 5, 7 are compared with errors of HPM [33] with N = 4 terms, Bessel collocation method [34] with N = 5, 7, CAS wavelet method [8] with k = 2, M = 1 , and differential transform method [9] with h = 0.1, n = 10. Errors obtained by our method are smaller than those of the Bessel collocation method [34] and HPM [33] for listed parameter values, which is also shown visually in Figure 1.…”

The Differential Transformation Method and Pade Approximant for a Form of Blasius Equation

“…For instances, Adomian decomposition method [1][2][3], homotopy perturbation method [3,4], variational iteration method [5,6,24]. The differential transform method [7][8][9][10][11][12][13][14][15] is one of the effective and reliable numerical solution methods for handling both linear and nonlinear differential equations.…”