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Lecture12A

# Lecture12A - Numerical Solution of Partial Differential...

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Numerical Solution of Partial Differential Equations (PDEs) EGN5455 Lecture 11 1

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Rationale: why? ± Most problems in science and ngineering involves rates of change engineering involves rates of change with respect to two or more dependent variables independent variables ± This leads to a PDE (or a set of PDEs) e will focus on 2 second order ± We will focus on 2-D, second order equations (methods can be generalized) 2
General form of PDEs 0 2 2 2 2 2 = + + + + + + G F E D C B A φ y x y y x x where A, B, C, D, E, F and G can be coefficients or nctions of ( functions of (x,y, ). This form of PDEs is very common as it often represents One of the conservation principles of physics (mass, momentum, energy, charge, etc). 3

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Types of PDEs ± Sommerfeld [1949] found that the aracter of PDEs changes radically character of PDEs changes radically depending on the sign of the “ iscriminant” B 2 - AC discriminant B 4AC ± “Elliptic” equations if B 2 -4AC < 0 arabolic” equations if B AC 0 ± “Parabolic” equations if B 2 -4AC = 0 ± “Hyperbolic” equations if B 2 -4AC > 0 4
Elliptic Equations ± They can be solved only by specifying

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Lecture12A - Numerical Solution of Partial Differential...

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