Homotopy perturbation method for predicting tsunami wave propagation with crisp and uncertain parameters

Abstract

Purpose The purpose of this paper is to find the solution of classical nonlinear shallow-water wave (SWW) equations in particular to the tsunami wave propagation in crisp and interval environment. Design/methodology/approach Homotopy perturbation method (HPM) has been used for handling crisp and uncertain differential equations governing SWW equations. Findings The wave height and depth-averaged velocity of a tsunami wave in crisp and interval cases have been obtained. Originality/value Present results by HPM are compared with the existing solution (in crisp case), and they are found to be in good agreement. Also, the residual error of the solutions is found for the convergence conformation and reliability of the present results.

Analytical solution of fuzzy heat problem in two-dimensional case under Caputo-type fractional derivative

“…The Homotopy perturbation scheme (HPS) was first proposed by He [24], which is the combination of the homotopy scheme and classical perturbation technique. In recent years, many researchers [25][26][27] studied the multiple forms of linear and nonlinear differential problems. Sene and Fall [28] used homotopy perturbation Laplace transform method to obtain the approximate solution of fractional diffusion equation and the fractional diffusion-reaction equation.…”

Gramian solutions and solitonic interactions of a (2+1)-dimensional Broer–Kaup–Kupershmidt system for the shallow water

“…Shallow water waves have been known as a type of the water waves with small depth relative to the water wavelength (Ablowitz, 2011). Investigations on the shallow water waves have been carried out in environmental engineering and hydraulic engineering (Ablowitz, 2011; Vreugdenhil, 1994; Zdyrski and Feddersen, 2021; Karunakar and Chakraverty, 2021; Salehipour et al , 2013; Wazwaz, 2019; Redor et al , 2019; Benkhaldoun et al , 2013; Shen and Tian, 2021; Chen et al , 2021; Chakravarty and Kodama, 2014). Certain nonlinear evolution equations (NLEEs) have been proposed to model the shallow water waves, such as the Korteweg–de Vries equation, Kadomtsev–Petviashvili-type equations, dispersive long-wave systems, Whitham–Broer–Kaup systems and Broer–Kaup–Kupershmidt (BKK) systems (Israwi and Kalisch, 2019; Das and Mandal, 2021; Crabb and Akhmediev, 2021; Hu et al , 2019; Shen et al , 2021; Ablowitz and Baldwin, 2012; Gao et al , 2021a; Ma et al , 2021a; Sulaiman et al , 2021; Liu et al , 2021; Wang et al , 2020; Ebadi et al , 2015; Zhao et al , 2021; Cheng et al , 2021; Al-Shawba et al , 2020; Wazwaz, 2013; Kumar et al , 2016; Wazwaz, 2021; Ying and Lou, 2001).…”