Two efficient computational technique for fractional nonlinear Hirota–Satsuma coupled KdV equations. Issue 2 (17th July 2020)

• Record Type: Journal Article
• Authors: Prakash, Amit; Verma, Vijay
• Is Part Of: Engineering computations. Volume 38:Issue 2(2021)
• Page Start: 791
• Page End: 818
• Publication Date: 2020-07-17
• Subjects: Hirota–Satsuma coupled KdV equation -- q-homotopy analysis Sumudu transform method -- Caputo fractional derivative -- Residual power series method; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-02-2020-0091
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this paper is to apply an efficient hybrid computational numerical technique, namely, q-homotopy analysis Sumudu transform method (q-HASTM) and residual power series method (RPSM) for finding the analytical solution of the non-linear time-fractional Hirota–Satsuma coupled KdV (HS-cKdV) equations. Design/methodology/approach: The proposed technique q-HASTM is the graceful amalgamations of q-homotopy analysis method with Sumudu transform via Caputo fractional derivative, whereas RPSM depend on generalized formula of Taylors series along with residual error function. Findings: To illustrate and validate the efficiency of the proposed technique, the authors analyzed the projected non-linear coupled equations in terms of fractional order. Moreover, the physical behavior of the attained solution has been captured in terms of plots and by examining the L 2 and L ∞ error norm for diverse value of fractional order. Originality/value: The authors implemented two technique, q-HASTM and RPSM to obtain the solution of non-linear time-fractional HS-cKdV equations. The obtained results and comparison between q-HASTM and RPSM, shows that the proposed methods provide the solution of non-linear models in form of a convergent series, without using any restrictive assumption. Also, the proposed algorithm is easy to implement and highly efficient to analyze the behavior of non-linear coupled fractional differential equation arisen in various area of science and engineering.