Author/Authors :
Nazari, Mojtaba UTM Centre for Industrial and Applied Mathematics, Malaysia , Barati, Vahid islamic azad university - Department of Mathematics, ايران , David, Vincent Daniel UTM Centre for Industrial and Applied Mathematics, Malaysia , David, Vincent Daniel Universiti Teknologi MARA - Faculty of Computer and Mathematical Sciences, Malaysia , Salah, Faisal UTM Centre for Industrial and Applied Mathematics, Malaysia , Salah, Faisal University of Kordofan - Faculty of Science - Department of Mathematics, Sudan , Abdul Aziz, Zainal UTM Centre for Industrial and Applied Mathematics, Malaysia , Abdul Aziz, Zainal Universiti Teknologi Malaysia - Faculty of Science - Department of Mathematics, Malaysia
Abstract :
This article presents a comparative study of the accuracy between homotopy analysis method (HAM) and a new technique of homotopy analysis method (nHAM) for the Korteweg–de Vries (KdV) and Burgers’ equations. The resulted HAM and nHAM solutions at 8th-order and 6th-order approximations are then compared with that of the exact soliton solutions of KdV and Burgers’ equations, respectively. These results are shown to be in excellent agreement with the exact soliton solution. However, the result of HAM solution is ratified to be more accurate than the nHAM solution, which conforms to the existing finding.
Keywords :
KdV equation , Burgers’ equation , homotopy analysis method , new homotopy analysis method , approximate analytic solution
