Analytical Approximations of Well Function by Solving the Governing Differential Equation Representing Unsteady Groundwater Flow in a Confined Aquifer

A solution of the governing equation representing drawdown in a horizontal confined aquifer, where groundwater flow is unsteady, was first provided by Theis and famously known as solution. This given terms an exponential integral, also called well function, for which simple reliable approximations are preferred due to their practical applications. To that end, several available literature, some based on series others numerical approximations. study employs three kinds homotopy-based methods, namely homotopy analysis method (HAM), perturbation (HPM), optimal asymptotic (OHAM), analytically solving partial differential (PDE). For convenience, PDE converted boundary value problem (BVP) using similarity transformation. Comparing obtained these methods with solution, it found 10th-order HAM, just OHAM-based solutions, provide accurate On other hand, HPM-based be only within small domain. Further, proposed compared literature percentage error. The methodology provides function directly general framework thus can adapted situations arising flow.