Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem

By Mehdi Dehghan, Fatemeh Shakeri. 2008

109 citations recorded by the source corpus.

In this paper, the solution of Cauchy reaction-diffusion problem is presented by means of variational iteration method. Reaction-diffusion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields. Application of variational iteration technique to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. Moreover, this technique does not require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computations.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7f027acc65d28b180e134fadb6d01734fc939547

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Citations in the corpus

The use of He's variational iteration method for solving the telegraph and fractional telegraph equations (2011, methodology): “The variational iteration method is used in [30] for solving the Lane–Emden equation, in [31] to solve several problems in calculus of variations, in [32] to find the solution of an inverse problem in partial differential equations, in [33] to solve a system of nonlinear integro-differential equatio”
Application of the Variational Iteration Method for System of Nonlinear Volterra’s Integro-Differential Equations (2009, methodology): “It was successfully applied to autonomous ordinary differential equation [4], to nonlinear partial differential equations with variable coefficients [5], to SchrödingerKDV, generalized KDV and shallow water equations [6], to Burgers' and coupled Burgers' equations [7], to the linear Helmoltz partial”
Redefined cubic B-splines collocation method for solving convection–diffusion equations (2012, methodology): “In [20] the solution of Cauchy reaction–diffusion problem is presented by means of variational iteration method.”
Solving nonlinear fractional partial differential equations using the homotopy analysis method (2010, methodology): “Wazwaz [23], examined the KdV, the K(2, 2), the Burgers, and the cubic Boussinesq equations by using variational iteration method (VIM) [40–51].”