Question

DIRECTIONS:
Part 1:
Set up a study about Partial Differential Equations (PDEs)
Discuss types and methods of solving the Differential Equation Equations (PDEs)
-             Elliptic Equations
-             Parabola equation
-             Hyperbola equation
Critically analyze the three PDEs indicating the possible boundary condition and make a comparison between them
Indicate how to drive the three equations: Explicit, implicit, and crank Nicolson.

Answer 1

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Perlial differential Equations (PDE5). method w PDES a'u the most common by odluichuul model physical problemas Finite elemuntsmethods are one engineering of many ways of solving PDES. Definition A PDE_is a Puelationship beteueen_an unknown function of several variables and its partial derivatives het u (2 02, ng, t) be an unknown function. au(21, M2, 83) as the dependent Variable Parist derivatuces Lau_denoted by zu Zu ani ana 274 an 2949 2²0 au , - 20 U2 = au 11 21 any ama Examples-To-Laplace_equalio'n t 50 => 26 + 2 + 20 = 0 any ? 21 2013 2._Poissor's Equations Q = P wluie pasowane donsily 3 _Heal_flow_equablon ! V = 1 od 1² at where 6² diffusivitu.

in all of its fald variables and linear PDE is one that is of first deo. & Non liniar PDES... Linear & Non liniar А doval partial For eg is linear 021 20-0 1712 2 2 ama is non linear 2014 Homogeneous PDES f_f09492, 9g, 1) = 0 hemegeneous the PDE is called 20 2 + 2u 2 is + au an is homogene 20 313 QU 24 +12 anz du 420 at any + is non- au 302 + There are 3 homogenu Ellipti, Hypeobolui_and_Parabolië PDES Lypes of second ondes PDE is mechanie's Thescase classified as elliptais hyperbole_and_parabolic The equations of elasticity ellipte Hyperboles - PDEs describe ivane The heat condution equalion is are PDE PI

Suppose all have second order PDE of the foom 2 2 a (1912) au + b(0,01) 204? Bu + C(M,2,34 ang 22 am? Id(492). au te (2, 2) out 2m ana f194?12) V = g (,m) Then PDE is called ellipki + b²-fac to flac PDE is called Layperbokit 6² 4ac to the PDE is calleol paraboli It b² - 400 =0

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