Solution Techniques for DQ Resultant Equations

Abstract

In most applications of the DQ method to engineering problems, which are governed by time-dependent partial differential equations (PDEs), the spatial derivatives are discretized by the DQ method whereas the time derivatives are discretized by low order finite difference schemes. For the general case, we consider a time-dependent PDE as follows $$ \frac{{\partial w}}{{\partial t}} + \ell \left( w \right) = g $$ (5.1) where l (w) is a differential operator containing all the spatial derivatives and g is a given function. Equation 5.1 should be specified with proper initial and boundary conditions for the solution to a specific problem.