Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation
نویسندگان
چکیده
The variational iterationmethod VIM 1–4 and homotopy perturbationmethod HPM 5– 8 , proposed byHe, are powerful analytical methods for various kinds of linear and nonlinear problems. For example, the variational iteration method has been applied to autonomous ordinary differential equation 9 and delay differential equation 10 . Abdou and Soliman applied this method to Schrodinger-KDV, generalized KDV, and Shallow water equations 11 , Burger’s equations, and coupled Burger’s equations 12 . Furthermore, Momani and Abuasad 13 used VIM for Helmoltz partial equation. Also homotopy perturbation methodwas successfully applied to Voltra’s integrodifferential equation 14 , boundary value problem 8 , nonlinear wave equations 15 , and so forth; see 16–20 . In this paper, we exert these methods for linear Sturm-Liouville eigenvalue and boundary value problems BVPs . A linear Sturm-Liouville operator has the form
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