The objective of this presentation is to illustrate that the use of a higher order basis can significantly reduce the size of the problem that needs to be solved numerically. Hence problems that require supercomputers to solve can be solved on desktop computers. These concepts will be utilized to illustrate the advantages for integral equation methodology and for the solution of complex problems using the finite element method. Even though these methodologies will be presented in terms of a frequency domain methodology, these principles can easily be applied to the solution of time domain problems where instead of using a sub sectional temporal basis functions, one can use a set of entire domain orthogonal functions resulting in an unconditional stability for any time domain methodologies. Illustrations will be made for Integral equations, however these principles hold for finite element and even finite difference time domain methodologies. © 2014 IEEE.