A new hybrid method called the combined hybrid method, to be used in solving the linear systems of equations capacitance transducer (SPCT) , is introduced and investigated. The SPCT has been employed in the measurement of the flow velocity in pneumatic conveyors used to convey solid materials. The new method combines the iterative SOR and the direct FFT method in a recursive process with the aim of facilitating the computation of the SPCT potential fields using personal computers. To accelerate the convergence of the method a technique of overlapping is arising from the finite difference approximation of Laplace's equation which describe the potential field of the space periodic introduced where the regions which are solved by the different SOR and FFT methods contain common rows between them (overlapped rows).Empirical investigations show that the convergence rate of the combined hybrid method will improve as the number of the overlapped rows is increased. The part of the system which represents the region of complex geometry will be solved using a simple iterative method like the SOR method while the remaining region will be solved using a fast complicated method like the FFT method. A significant improvement in the computation speed has been gained when this method is used and it has been found that its performance is better than the ordinary SOR method especially when an adaptive threshold technique, which has been introduced in this work, is adopted as a stopping criterion for the SOR method which is used in the combined method. The method has been implemented on a PC to obtain the electrostatic potential distribution for an SPCT both in the no flow condition and in the presence of a dielectric stimulus. A grid of 40x149 nodes was used to model the SPCT. Plots of equipotential contours for the SPCT have also been obtained.