The behaviour of the maximum and minimum error for Fredholm-Volterra integral equations in two-dimensional space

An Algorithm for the Closed-Form Solution of Certain Classes of Volterra–Fredholm Integral Equations of Convolution Type

“…Collocation methods are very popular. They are based on splines [21,29,92,93], general approximate functions [22,82], Chebyshev polynomials [16], shifted Chebyshev polynomials [81], Bernstein polynomials [34,63], Chelyshkov Polynomials [36], Lagrange polynomials [42], Taylor polynomials [47], Fibonacci polynomials [57], Bell polynomials [65], first Boubaker polynomials [60], Müntz-Legendre polynomials [70], generalized Lucas polynomials [87], Jacobi polynomials [89], block-pulse functions [27], hybrid of block-pulse functions and Lagrange polynomials [26], hybrid block-pulse function and Taylor polynomials [41] (see also [73]), block-pulse functions and Bernoulli polynomials [45], hybrid block-pulse functions and Bernstein polynomials [62], Haar wavelets [4,66], rationalized Haar functions [19], Legendre wavelets [13,97], triangular functions [23,100], fuzzy transforms [32], Sinc function [37,40], radial basis functions [35], pseudospectral integration matrices [54] and shifted piecewise cosine basis functions [75]. Galerkin methods are also popular and are commonly used in conjunction with general approximate functions [22,82], Legendre polynomials…”

On the Solutions of the Second Kind Nonlinear Volterra-Fredholm Integral Equations via Homotopy Analysis Method

“…In the application of physical mathematics and engineering, the second kind of NV-FIEs are often arisen [1][2][3][4][5][6][7][8]. Therefore, there exist great efforts to approximate the solution of this kind of NV-FIEs.…”

“…shows the behaviour of error using HAM at n = 10 and h = −1.9, t ∈ [0, 0.8]. Also, Fig (2). presents the valid region of h at n = 10.…”

A new Model for Solving Three Mixed Integral Equations with Continuous and Discontinuous Kernels

“…The solution of the MIE of the first kind in one, two and three dimensions has been obtained analytically using the separation of variables method in [1]. The MIE of the first kind can be solved analytically using one of the following methods: The Cauchy method, orthogonal polynomial method, potential theory method and Krein's method, see [9][10][11][12][13][14][15][16] and the references therein for details. The relation between the MIEs and some contact problems can be found in [13][14][15][16][17] and the references therein.…”

“…The MIE of the first kind can be solved analytically using one of the following methods: The Cauchy method, orthogonal polynomial method, potential theory method and Krein's method, see [9][10][11][12][13][14][15][16] and the references therein for details. The relation between the MIEs and some contact problems can be found in [13][14][15][16][17] and the references therein. This work is a new contribution, to the best of our knowledge, in this active area of scientific research.…”