Solution of delay differential equations via a homotopy perturbation method

By Fatemeh Shakeri, Mehdi Dehghan. Mathematical and computer modelling, 2008

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A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed‐order fractional damped diffusion‐wave equation (2018, unknown): “Also, relation (34) by changing index from  to n can be changed to ‖∇en‖L2(Ω) ≤ ‖‖∇e0‖‖L2(Ω) + 2τ n ∑ k=1 ‖‖‖∇ek−m‖‖‖L2(Ω) ≤ ‖‖∇e0‖‖L2(Ω) + 2τ 0 ∑ k=−m ‖‖‖∇ek−m‖‖‖L2(Ω) + 2τn−m ∑ k=1 ‖‖‖∇ek‖‖‖L2(Ω) ≤ ‖‖∇e0‖‖L2(Ω) + 2τ 0 ∑ k=−m ‖‖‖∇ek−m‖‖‖L2(Ω) + 2τn−1 ∑ k=1 ‖‖‖∇ek‖‖‖L2(Ω).”
THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS (2012, methodology): “Also we refer the interested reader to [8,9,39,41] for some basic ideas in Adomian decomposition method, the variational iteration method, homotopy perturbation method and the homotopy analysis method, respectively.”
Solution of Delay Differential Equation by Means of Homotopy Analysis Method (2009, methodology): “Shakeri and Dehghan [6] used the homotopy perturbation method (HPM) to obtain the approximate solution for the initial value problem of DDE.”
A spectral element approach for the stability of delay systems (2011, background): “The initial guess x0 can be assigned freely [18]; however, a good initial approximation can accelerate convergence [28].”