Modeling and simulation Elliptical 2nd order linear P.D.E using COMSOL Multiphysics | ||||
| The International Undergraduate Research Conference | ||||
| Volume 6, Issue 6, September 2022, Page 1-8 PDF (1 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/iugrc.2022.302457 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| Ahmed Saeed farg Hassan | ||||
| Higher institute of engineering and technology fifth settlement, Egypt. | ||||
| Abstract | ||||
| 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; Elliptic equations reduce to a form coinciding with the Laplace’s equations Thus, Laplace’s equations serve as basic canonical models for all Elliptical second order linear PDEs the reduced canonical form can be modeled by boundary condition with COMSOL Multiphysics and Mathematica elliptical PDEs serve as basic uniform steady state solution for analysis of both parabolic and hyperbolic PDES. | ||||
| Keywords | ||||
| elliptical PDEs; canonical form; constant coefficient PDEs; variable coefficients PDEs; LaPlace equation | ||||
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