Solution of interval shallow water wave equations using homotopy perturbation method

Abstract

PurposeThis paper aims to present solutions of uncertain linear and non-linear shallow water wave equations. The uncertainty has been taken as interval and one-dimensional interval shallow water wave equations have been solved by homotopy perturbation method (HPM). In this study, basin depth and initial conditions have been taken as interval and the single parametric concept has been used to handle the interval uncertainty.Design/methodology/approachHPM has been used to solve interval shallow water wave equation with the help of single parametric concept.FindingsPreviously, few authors found solution of shallow water wave equations with crisp basin depth and initial conditions. But, in actual sense, the basin depth, as well as initial conditions, may not be found in crisp form. As such, here these are considered as uncertain in term of intervals. Hence, interval linear and non-linear shallow water wave equations are solved in this study using single parametric concept-based HPM.Originality/valueAs mentioned above, uncertainty is must in the above-titled problems due to the various parametrics involved in the governing differential equations. These uncertain parametric values may be considered as interval. To the best of the authors’ knowledge, no work has been reported on the solution of uncertain shallow water wave equations. But when the interval uncertainty is involved in the above differential equation, then direct methods are not available. Accordingly, single parametric concept-based HPM has been applied in this study to handle the said problems.