In this paper, a comparative study between two different methods for solving nonlinear Caputo time-fractional wave-like equations with variable coefficients is conducted. These two methods are called the Shehu variational iteration method (SVIM) and the Shehu decomposition method (SDM). To illustrate the efficiency and accuracy of the proposed methods, three different numerical examples are presented. The results obtained show that the two methods are powerful and efficient methods which both give approximations of higher accuracy and closed form solutions if existing. However, the SVIM has an advantage over SDM that it solves the nonlinear problems without using the Adomian polynomials. Furthermore, the SVIM enables us to overcome the difficulties arising in identifying the general Lagrange multiplier and it may be considered as an added advantage of this technique over the SDM.
Khalouta, Ali and Kadem, Abdelouahab
A Comparative Study of Shehu Variational Iteration Method and Shehu Decomposition Method for Solving Nonlinear Caputo Time-Fractional Wave-like Equations with Variable Coefficients,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
1, Article 24.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/24