It is often possible to transform a partial differential equation (PDE) into an ordinary differential equation (ODE) through an appropriate change of variables. However, the resulting ODE is not always solvable in terms of elementary functions. In such cases, numerical methods are typically employed to solve the reduced ODE. As yet, there are no established systematic procedures for using these numerical solutions to reconstruct the solution of the original PDE. This work demonstrates a systematic approach to address such situations.