A method for the calculation of electronic continuum wave functions is presented which is based on the logarithmic derivative version of the Kohn (LDK) variational principle. The variational principle is cast into algebraic form by introducing a finite basis set that consists of spherical harmonic Gaussian-type functions (GTOs) and of Lobatto shape functions with the latter representing the translational part of the basis. A local effective potential which is obtained from density functional theory results in fairly accurate photoionization cross sections. Also studied are asymptotic corrections to the effective potential for the photoelectron which, in many cases, lead to improved results. The Lobatto procedure is applied to the diatomics N-2 and CO and to benzene which may be regarded as a prototype for larger non spherical symmetric systems for which the method is targeted. For the two diatomics, results in excellent agreement with experiment have been found. For benzene the results are compared to those obtained by the Stieltjes-Tchebychev (ST) imaging technique and by the continuum multiple scattering (CMS) method which both have been applied to similar effective local potentials. Comparison with the ST imaging technique shows that the LDK Lobatto (LDKL) method provides qualitatively similar results, but the LDKL cross sections are of higher resolution and allow a more detailed analysis because of the explicit determination of the continuum wave function. For most of the valence orbitals of benzene the CMS method does not lead to satisfactory agreement with experiment due to the well-known deficiencies of this technique. The LDKL method implemented with a combined basis set does not suffer from the limitations of the ST and the CMS methods, but remains applicable to larger-size molecules.