ABSTRACT
Real-world modeling depends on many variables simultaneously. So, when we try to model some phenomena from the real world with the help of ordinary differential equations (ODE), we restrict our analysis to one independent variable (namely, time) only. That is, we only succeed in describing the dynamical behavior of the problem of interest with respect to that independent variable. Thus, using ODE models means that we are considering that independent variable, which is the most important factor affecting the problem of interest, and other factors are taken to be negligible. Because of this restriction, ODE models often fail to reflect the dynamics as shown by the acted phenomena. Thus, a disparity between an ODE model and data may signify that its state variables depend on more than one independent variable (say, time and space). Hence, instead of using an ODE model in such cases, it may be appropriate to use a partial differential equation (PDE) model.
