We present an approach to uncoupling the pair of transient governing equations used in electrokinetics (i.e., streaming potential and electroosmosis). This approach allows for the solution of two uncoupled “intermediate” equations, then the physical solution is found by recombination of these intermediate potentials through a matrix multiplication. We present numerically stable expressions for the coefficients, and an example showing electrokinetics arising from pumping a fully penetrating well in a confined aquifer, surrounded by insulating aquicludes. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. (SAND2019-8712 A)