Variational Iteration Method for Delay Differential-Algebraic Equations

Abstract

Variational iteration method is applied to solve a class of delay differentialalgebraic equations. The obtained sequence of iteration is based on the use of Lagrange multipliers. The corresponding convergence results are obtained and successfully confirmed by some numerical examples.

Convergence of Variational Iteration Method for Fractional Delay Integrodifferential‐Algebraic Equations

“…When = 1, system (1) can be written as the delay integrodifferential-algebraic equation. Moreover, if the right function of system (1) has no integral item, it becomes the delay differential-algebraic equation discussed in [35].…”

“…The variational iteration method (VIM) is one of the important methods used to obtain approximate analytical solutions [22][23][24][25] and possesses some good properties, such as flexibility, convenience, accuracy, and less storage. In particular, this method was used to solve pantograph equations [26,27], differential (integral) equations [28][29][30], fractional differential (integral) equations [31][32][33][34], delay differentialalgebraic equations [35] and fractional differential-algebraic equations [36], and so forth.…”

Convergence of Variational Iteration Method for Second-Order Delay Differential Equations

“…The variational iteration method (VIM) was first proposed by He [4,5] and has been extensively applied due to its flexibility, convenience, and efficiency. So far, the VIM is applied to autonomous ordinary differential systems [6], pantograph equations [7], integral equations [8], delay differential equations [9], fractional differential equations [10], the singular perturbation problems [11], and delay differential-algebraic equations [12]. Rafei et al [13] and Marinca et al [14] applied the VIM to oscillations.…”