© 2020, Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature.In this paper, the solution of nonlinear forced convection in a porous saturable duct is numerically approximated by two different approaches. The first one is a Lie group integrator based on the group SL2(R) , whose calculation is far simpler and easier. The second method is reproducing kernel Hilbert space (RKHS) method which uses the Hilbert spaces in calculation. Convergence analyses for both methods were done. Effects of the porous media shaped parameter, Forchheimer number, and viscosity ratio on the solutions are discussed and illustrated by the proposed methods. The numerical experimentsshowed that the SL2(R) -shooting method and RKHS method are suitable for solving the forced convection in a porous-saturated duct with high accuracy and efficiency.