Ali. F. Jameel^1,*, N. R. Anakira², A. K. Alomari³, Noraziah H. Man¹

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.3, pp. 875-899, 2021, DOI:10.32604/cmes.2021.014460

Abstract Homotopy Analysis Method (HAM) is semi-analytic method to solve the linear and nonlinear mathematical models which can be used to obtain the approximate solution. The HAM includes an auxiliary parameter, which is an efficient way to examine and analyze the accuracy of linear and nonlinear problems. The main aim of this work is to explore the approximate solutions of fuzzy Volterra integral equations (both linear and nonlinear) with a separable kernel via HAM. This method provides a reliable way to ensure the convergence of the approximation series. A new general form of HAM is presented and analyzed in the fuzzy… More >

Mustafa Turkyilmazoglu^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.120, No.1, pp. 63-81, 2019, DOI:10.32604/cmes.2019.06858

Abstract A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications. It was shown in the latter through various comparative physical models that the ratio approach of identifying the range of the convergence control parameter and also an optimal value for it in the homotopy analysis method is a promising alternative to the classically used h-level curves or to the minimizing the residual (squared) error. A mathematical analysis is targeted here to prove the equivalence of both the ratio approach and the traditional residual approach, especially… More >