Consider the integralwhere x1, x2, …, xN are jointly distributed in a multivariate normal distribution f(x1, x2, …, xN) with (pij) as the correlation matrix. The integral has been expressed in an infinite series of tetrachoric functions for N≥2. The infinite series is not only complicated, but also is very slowly convergent and is consequently not of much practical use. Plackett (8) obtains a reduction formula for expressing normal integrals in four variates as a finite sum of single integrals of tabulated functions. These integrals have then to be evaluated by a rather awkward numerical quadrature.

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<p>Understanding the complex groundwater flow behaviour is of utmost importance for a better and quicker management of groundwater. A thorough study of flow behaviour can be attained by modeling. Numerical simulation models have been proven to be an effective means of modeling of groundwater. The state-of-art meshfree simulation models, demonstrated in the various studies, have a clear advantage of allaying the meshing and remeshing complications. Meshless methods can be grouped into weak, strong and weak strong form methods. The strong form methods are truly meshfree, straightforward and efficacious, but they require a special treatment for the derivative boundaries. This imposes a limitation on the strong form methods in the application of groundwater studies, as the aquifers predominantly involve natural boundary conditions. The weak form methods, though effective in handling the derivative boundary conditions, require more computational time. The meshless weak strong (MWS) form combines the strengths of the strong and weak forms to obtain efficient and robust solutions with a lesser computational cost. This study aims at investigating the unexplored area of the applicability of the theoretically potent MWS method to the groundwater flow problems. In this context, the MWS model is developed by integrating the Meshless Local Petrov Galerkin (MLPG) method and the Radial Point Collocation Method (RPCM). The developed MWS model is applied to the flow studies in a hypothetical confined aquifer and is observed to result in fruitful solutions. Highlighting the advantages of the MWS method, satisfactory results could be obtained in atleast 30% lesser computational time compared to the weak form model. Thus, MWS method can be considered as an efficient tool to simulate large scale groundwater flow problems.</p>