Modeling and simulation hyperbolic 2nd order linear P.D.E using COMSOL Multiphysics

The Partial Differential Equations (PDEs) are very important in dynamics, aerodynamics, elasticity, heat transfer, waves, electromagnetic theory, transmission lines, quantum mechanics, weather forecasting, prediction of disasters, how universe behave ……. Etc., second order linear PDEs can be classified according to the characteristic equation into 3 types coinciding 3 basic conic sections hyperbolic, parabolic and elliptic; Elliptic equations have none family of (real) characteristic curves. All the three types of equations can be reduced to its first canonical form finding the general solution or the second canonical form similar to 3 basic PDE models; Hyperbolic equations have two distinct families of (real) characteristic curves. Hyperbolic type of equations can be reduced to its first canonical form finding the general solution or the second canonical form similar to basic PDE models; Hyperbolic equations reduce to a form coinciding with the wave equation. Thus, the wave equation serves as basic canonical models for all second order hyperbolic linear P.D.E the reduced canonical form can be modeled by initial and boundary condition with COMSOL Multiphysics allowing the analysis of physical phenomena to predict the variance over time for different types of transmission line ( RG59, CAT5, PIC, EXL-120, …… ) as shown in tables of fig (5,7,8,11) used for different electrical applications data transmission, audio and video transmission, signal transmission…etc..