In this paper the mathematical model of moisture content in soil have been designed in the form of three-dimensional nonlinear PDEs. The analytical solution of model equation has been obtained by using the combine LA-transform with decomposition method. The accuracy and efficiency of suggested method is illustrated by three problems.

In this paper, efficient modification of Adomain decomposition method is proposed to solve nonlinear partial differential equations. Yields solution in rapid convergent series from easily computable terms to get exact solution, and yields in few iterations we get exact solution. Moreover, this modification does not require any linearization, discretization, or perturbations and therefore reduces the computations. Two illustration examples are introduced and illustrate the procedure of modification is simple yet highly accurate and rapidly converge to exact solution compares with the ADM or other modifications. The methodology presented here is useful for strongly nonlinear problems.

This paper presents an analysis solution for systems of partial differential equations using a new modification of the decomposition method to overcome the computational difficulties. Convergence of series solution was discussed with two illustrated examples, and the method showed a high-precision, being a fast approach to solve the non-linear system of PDEs with initial conditions. There is no need to convert the nonlinear terms into the linear ones due to the Adomian polynomials. The method does not require any discretization or assumption for a small parameter to be present in the problem. The steps of the suggested method are easily implemented, with high accuracy and rapid convergence to the exact solution, compared with other methods that can be used to solve systems of PDEs.

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