Numerical implementation of Adomian decomposition method for linear Volterra integral equations of the second kind

A new approach to the numerical solution of Volterra integral equations by using Bernstein’s approximation

“…There are many numerical methods for solving Volterra integral equations of the second kinds [7]; Maleknejad and Aghazadeh in [8] obtained a numerical solution of these equations with convolution kernel by using Taylor-series expansion method, in [9] Maleknejad, Tavassoli and Mahmoudi produced a method for numerical solution of Volterral integral equation of the second kind by using legendre wavelet, in [10] Babolian and Davari solved the integral equation numerically based on Adomian decomposition method, Rashidinia and Zarebnia [11] obtained a numerical solution of the integral equation by Sinc-collection method, in [12] Saberi and Heidari used a quadratic method with variable step for solving these equations, and recently in [13] Tahmasbi solved linear Volterra integral equations of the second kind based on the power series method.…”

The variational iteration method for solving the fractional coupled lotka-volterra equation

“…He [2,3].This method has been widely used for solving the analytic solutions of physically signifi cant equations arranging from linear to nonlinear, from ordinary diff erential to partial diff erential, form integer to fractional, et.al [2,3,4,8,15,16,17,18,19,20]. The idea of VIM is to construct correction functionals using general Lagrange multupliers identifi ed optimally via the variational theory, and the initial approximations can be freely chosen with unknown constants.…”

Solving Nonlinear Volterra | Fredholm Integro-differential Equations Using the Modified Adomian Decomposition Method

“…The standard decomposition technique represents the solution of u in (2.1) as the following series: 5) where, the components u 0 , u 1 , . .…”

“…(1.1) reduces to the following equation: Since many physical problems are modeled by integro-differential equations, the numerical solutions of such integro-differential equations have been highly studied by many authors. In recent years, numerous works have been focusing on the development of more advanced and efficient methods for integral equations and integro-differential equations such as the lineaziation method [1], the differential transform method [2], RF-pair method [3], and semianalytical-numerical techniques such as the Adomian decomposition method [5] and Taylor polynomials method [4,[6][7][8]. The modified decomposition method for solving nonlinear Volterra -Fredholm integral equations was presented by Bildik and Inc in [9].…”