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**A residual power series technique for solving Boussinesq-Burgers equations.**
*(English)*
Zbl 1438.35363

Summary: In this paper, a residual power series method (RPSM) is combining Taylor’s formula series with residual error function, and is investigated to find a novel analytical solution of the coupled strong system nonlinear Boussinesq-Burgers equations according to the time. Analytical solution was purposed to find approximate solutions by RPSM and compared with the exact solutions and approximate solutions obtained by the homotopy perturbation method and optimal homotopy asymptotic method at different time and concluded that the present results are more accurate and efficient than analytical methods studied. Then, analytical simulations of the results are studied graphically through representations for action of time and accuracy of method.

### MSC:

35Q53 | KdV equations (Korteweg-de Vries equations) |

35C10 | Series solutions to PDEs |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

94A20 | Sampling theory in information and communication theory |

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\textit{B. A. Mahmood} and \textit{M. A. Yousif}, Cogent Math. 4, Article ID 1279398, 11 p. (2017; Zbl 1438.35363)

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### References:

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