资源环境科技发展态势分析平台

In this work we consider the Boussinesq equation applied to a one-dimensional homogeneous aquifer with constant boundary conditions. Such a problem is generally solved (both analytically and numerically) by transforming it from a boundary value problem into an equivalent initial value problem that has to be solved by means of a trial-and-error approach. We devise a method that eliminates the need for trial and error that is purely analytical, which can benefit both numerical and analytical solutions. Furthermore, we present a general series solution that solves this equation analytically with arbitrary precision. The series solution generalizes two particular cases that already exist in the literature. With the new proposed series, the need for any numerical integration of differential equations is removed, and fully analytical benchmark solutions are obtained.