Some Relatively New Techniques for Nonlinear Problems
By Syed Tauseef Mohyud-Din, Muhammad Aslam Noor, Khalida Inayat Noor. 2009
163 citations recorded by the source corpus.
This paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems of physical nature. In particular, we will focus on the variational iteration method (VIM) and its modifications, the homotopy perturbation method (HPM), the parameter expansion method, and exp-function method. These relatively new but very reliable techniques proved useful for solving a wide class of nonlinear problems and are capable to cope with the versatility of the physical problems. Several examples are given to reconfirm the efficiency of these algorithms. Some open problems are also suggested for future research work.
Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/667a40891dc5deca8854655a3943428a97be26c4
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Citations in the corpus
- Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation (2019, background): “Thus, Equation (41) gives an approximate solution to problem (37) in terms of convergence parameters h and n.”
- Exact and solitary wave solutions for the Tzitzeica-Dodd-Bullough and the modified KdV-Zakharov-Kuznetsov equations using the modified simple equation method (2013, methodology): “transformation method [5,6], the tanh-function method [7,8], the (G0/G)-expansion method [9–16], the Exp-function method [17–20], the modified simple equation method [21–23], the variational iteration method [25–27] and the homotopy perturbation method [28,29], and so on.”