Applied Mathematics & Information Sciences

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In this study, we propose a novel combination method between the ARA integral transform and the homotopy perturbation approach to solve systems of nonlinear partial differential equations. The difficulty arising in solving nonlinear partial differential equations could simply be overcome by using He’s polynomials during the application of the new method. The proposed technique can provide the solutions of the target problems without pre-assumptions or restrictive constrains in addition to avoiding the round-off errors. The efficiency of the new method is illustrated by applying it to solve different examples of systems of nonlinear partial differential equations. We discuss three interesting applications and solve them by the new approach, called ARA-homotopy perturbation method and get exact solutions, also the results are illustrated in figures.

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