Variational Iterative Method

Abstract

Variational iterative method (VIM) is again a semi-analytical technique like homotopy perturbation method (HPM) and Adomian decomposition method (ADM) for solving both linear and nonlinear ordinary/partial/fractional differential equations. This technique is based on the application of restricted variations and correction functional. VIM does not require small parameters in the differential equation and generates a solution as a sequence of iterations. It does not need the nonlinearities to be differentiable with respect to the dependent variable and its derivatives. This chapter first discusses the fundamental concept of VIM. Further, this method is used to deal with two problems: a linear one-dimensional fractional heat-like equation and a nonlinear fractional advection equation. The test problems used in this chapter indicate that VIM is an effective way to solve linear/nonlinear fractional differential equations. The series generally converges with an increase in terms, but the compact solution form may not always be expected.

Cite this paper

@misc{chakraverty2022variational,
  title = {{Variational Iterative Method}},
  author = {Chakraverty, Snehashish and Jena, Rajarama Mohan and Jena, Subrat Kumar},
  pages = {101--108},
  year = {2022},
  doi = {10.1002/9781119697060.ch9}
}

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