Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment

Abstract

In this manuscript, a new hybrid technique viz Sawi transform-based homotopy perturbation method is implemented to solve one-dimensional shallow water wave equations. In general, the quantities involved with such equations are commonly assumed to be crisp, but the parameters involved in the actual scenario may be imprecise/uncertain. Therefore, fuzzy uncertainty is introduced as an initial condition. The main focus of this study is to find the approximate solution of one-dimensional shallow water wave equations with crisp, as well as fuzzy, uncertain initial conditions. First, by taking the initial condition as crisp, the approximate series solutions are obtained. Then these solutions are compared graphically with existing solutions, showing the reliability of the present method. Further, by considering uncertain initial conditions in terms of Gaussian fuzzy number, the governing equation leads to fuzzy shallow water wave equations. Finally, the solutions obtained by the proposed method are presented in the form of Gaussian fuzzy number plots.

Numerical investigation of two-dimensional fuzzy fractional heat problem with an external source variable

“…Definition 2.3 The Sawi transform is defined as [ 26 ] where ω shows the transformation variable. If ϑ (℘) is exponentially ordered and piecewise continuous, then the ST of the function ϑ ( τ ), τ ≥ 0 exists; otherwise, ST might not exist.…”

A study of time-fractional model for atmospheric internal waves with Caputo-Fabrizio derivative

“…Tamboli and Tandel [ 15 ] applied reduced differential transform method for the treatment of internal atmospheric waves phenomenon. Sahoo and Chakraverty [ 16 ] used Sawi transformn based homotopy perturbation method to solve shallow-water equation in fuzzy environment. Sartanpara and Meher [ 17 ] examined the differential equation system representing the atmospheric internal waves by using q-homotopy analysis Shehu transform method.…”

On Hilfer-Prabhakar fractional derivatives Sawi transform and its applications to fractional differential equations

“…In 2019, Mahgoub et al [17] introduced a new integral transform called the Sawi transform, with the main purpose of studying its applicability for solving linear differential equations. Nowadays, the Sawi transform is widely used by researchers in science and engineering to solve various problems for integral and differential equations [24][25][26][27][28][29].…”