The variational iteration method for solving nonlinear Volterra's integro-differential equations
طريقة التغاير التكراري (VIM) لحل معادلات فولتيرا التكاملية التفاضلية غير الخطية
DOI:
https://doi.org/10.36602/jsba.2026.22.04Abstract
In this paper, we present some basic ideas of the Variational Iteration Method (VIM) for solving nonlinear Volterra integro-differential equations. The Variational Iteration Method is used to solve a wide range of nonlinear problems efficiently, easily, and accurately, with approximations that converge rapidly to precise solutions. For linear problems, the exact solution can be obtained in just one iteration step due to the possibility of identifying the Lagrange multiplier accurately. It is worth noting that the Lagrange multiplier reduces the number of iterations on the integral operator, as well as the volume of computational operations. The method does not require any kind of transformation or linearization. Numerical examples are provided to highlight the significant features of the (VIM) method. The method shows improvements over current numerical techniques.
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