On Finding Exact Solutions to Coupled Systems of Partial Differential Equations by the NDM

Mahmoud Saleh Rawashdeh, Shehu Maitama


In this article, we develop a
new method called the Natural Decomposition Method (NDM). We use the
NDM to find exact solutions for coupled systems of linear and
nonlinear partial differential equations. The proposed method is a
combination of the Natural Transform Method (NTM) and Adomian
Decomposition method (ADM). Besides, the NDM avoid round-off errors
which leads to solutions in closed form. The new method always lead
to an exact or approximate solution in the form of rapidly
convergence series. Hence, the Natural Decomposition Method is
elegant refinement of the existing methods and can easily be used
to solve a wide class of Linear and Nonlinear Partial Differential Equations.
{\bf Keywords:} Natural Decomposition Method, Adomian polynomials,
Coupled System Partial Differential Equations.


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