The plot illustrating the NPDE
is shown in Figure 4.
In the nonlinear science, many important phenomena in various fields can be described by the nonlinear partial differential equations (NPDEs).
It is well known that NPDEs with variable coefficients are more realistic in various physical situations than their constant coefficients counterparts.
The rest of this paper is organized as follows: in Section 2, we will describe the auxiliary equation method for finding out solutions of variable-coefficient NPDEs and give the main steps of the method here.
In this case the tolerances are scalar values (as specified by S2D_Scalar_TOL), but for PDE systems the user will usually supply vectors of length npde in order to apply different tolerances to each PDE variable.
A refinement indicator for the jth triangle is defined by an average scaled error ([serr.sub.j]) measurement over all npde PDEs
Many phenomena in physics, engineering, and science are described by nonlinear partial differential equations (NPDEs
In the recent years, investigations of exact solutions to nonlinear partial differential equations (NPDEs
) play an important role in the study of nonlinear physical phenomena.
The evolution of local and state runoff controls have received impetus from the EPA National Pollutant Discharge Elimination System (NPDES
) Phase II storm water regulations.