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**Laplace Adomian decomposition method to study chemical ion transport through soil.**
*(English)*
Zbl 1416.35013

Summary: The paper deals with a theoretical study of chemical ion transport in soil under a uniform external force in the transverse direction, where the soil is taken as porous medium. The problem is formulated in terms of boundary value problem that consists of a set of partial differential equations, which is subsequently converted to a system of ordinary differential equations by applying similarity transformation along with boundary layer approximation. The equations hence obtained are solved by utilizing Laplace Adomian Decomposition Method (LADM). The merit of this method lies in the fact that much of simplifying assumptions need not be made to solve the non-linear problem. The decomposition parameter is used only for grouping the terms, therefore, the nonlinearities is handled easily in the operator equation and accurate approximate solution are obtained for the said physical problem. The computational outcomes are introduced graphically. By utilizing parametric variety, it has been demonstrated that the intensity of the external pressure extensively influences the flow behavior.

### MSC:

35A22 | Transform methods (e.g., integral transforms) applied to PDEs |

35A25 | Other special methods applied to PDEs |

35Q40 | PDEs in connection with quantum mechanics |

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\textit{P. Soni} et al., Appl. Appl. Math. 14, No. 1, 475--484 (2019; Zbl 1416.35013)

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### References:

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