The convergence of He’s variational iteration method for solving integral equations

Abstract

a b s t r a c tIn this paper, several integral equations are solved by He's variational iteration method in general case, then we consider the convergence of He's variational iteration method for solving integral equations.Crown

Operator Equation and Application of Variation Iterative Method

“…In this Letter, we consider operator equations and apply the variation iteration method to integral-differential equations, and extend some results in [3,8,10]. The obtained solution shows the method is also a very convenient and effective for various integral-differential equations, only one iteration leads to exact solutions.…”

“…In this section, we apply the variation iteration method (simple writing VIM) to Integral equations bellow (see [8,9]). To illustrate the basic idea of the method, we consider:…”

Variational iteration method for singular perturbation initial value problems

“…Wazwaz [1] used the VIM for analytic treatment of linear and nonlinear ODEs. Saadatmandi, Dehghan [2] and Yu [21] applied the VIM to solve pantograph equations. Xu [14], Saadati, Dehghan, Vaezpour and Saravi [20] considered the convergence of VIM for solving integral equations.…”

“…Saadatmandi, Dehghan [2] and Yu [21] applied the VIM to solve pantograph equations. Xu [14], Saadati, Dehghan, Vaezpour and Saravi [20] considered the convergence of VIM for solving integral equations. Though Darvishi, Khani and Soliman [16] applied the VIM to some stiff ODEs, but these stiff problems do not contain the singular perturbation problems.…”

Variational Iteration Method for Singular Perturbation Initial Value Problems with Delays

“…Starting from pioneering ideas going back to Inokuti-Sekine-Mura method [3], the variational iteration method was first proposed in later 1990s by He [4][5][6]. By recent years, this method has been extensively applied to various ODEs, integral equations, delay differential equations and fractional differential equations, two-point boundary value problems, oscillations, and stiff ODEs, notably, He [7,8], Wazwaz [9,10], Draganescu et al [11,12], Saadatmandi and Dehghan [13], Salkuyeh [14], Lu [15], Xu [16], Rafei et al [17], Darvishi et al [18], Tatari and Dehghan [19], Mamode [20], Saadati and Dehghan [21], Yu [22], Marinca et al [23], Yang and Dumitru [24], and Wu [25] to mention only a few. Recently, Zhao and Xiao [26] have applied this method for solving singular perturbation initial value problems.…”