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SITUATION 1 Classify the following PDES as either elliptic, parabolic, or hyperbolic. Notation: • u, = first partial derivative of u(x, y) with respect to x %3! Uy = first partial derivative of u(x, y) with respect to y • Ux = second partial derivative of u(x, y) with respect to x %3! Uyy = second partial derivative of u(x, y) with respect to y • Uny = second partial derivative of u(x, y) with respect to x and y • Ugy = Uyx %3D Uzz + 5 (uz + uy) – u = 1

SITUATION 1 Classify the following PDES as either elliptic, parabolic, or hyperbolic. Notation: • u, = first partial derivative of u(x, y) with respect to x %3! Uy = first partial derivative of u(x, y) with respect to y • Ux = second partial derivative of u(x, y) with respect to x %3! Uyy = second partial derivative of u(x, y) with respect to y • Uny = second partial derivative of u(x, y) with respect to x and y • Ugy = Uyx %3D Uzz + 5 (uz + uy) – u = 1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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plssss answer both even if shortcut help plsss...... im beggin

SITUATION 2 Consider the following PDE: sin(2x) + cos(2y), = [0, , y= = [0, ) %3D I %3D The boundary conditions for the given domain are as follows: u (x = 0, y) = u (, y = ) = 1 %3D (x=, y) = (, y = du 3 du (2, y = 0) = 1 For solutions using finite difference method, the domain should be divided such that there will be three segments along x- and y-directions. (a) Derive the governing finite difference equation for the given PDE. (b) Considering the given boundary conditions, set-up the system of equations that would solve for the values of u(x, y) at the mesh points with unknown values.
Transcribed Image Text:SITUATION 2 Consider the following PDE: sin(2x) + cos(2y), = [0, , y= = [0, ) %3D I %3D The boundary conditions for the given domain are as follows: u (x = 0, y) = u (, y = ) = 1 %3D (x=, y) = (, y = du 3 du (2, y = 0) = 1 For solutions using finite difference method, the domain should be divided such that there will be three segments along x- and y-directions. (a) Derive the governing finite difference equation for the given PDE. (b) Considering the given boundary conditions, set-up the system of equations that would solve for the values of u(x, y) at the mesh points with unknown values.
SITUATION 1 Classify the following PDES as either elliptic, parabolic, or hyperbolic. Notation: • u, = first partial derivative of u(x, y) with respect to x %3D = first partial derivative of u(x, y) with respect to y • Uy • Uux = second partial derivative of u(x, y) with respect to x = second partial derivative of u(x, y) with respect to y %3D Uyy Uxy = second partial derivative of u(x, y) with respect to x and y • Ugy = Uyx %3D Uzz + 5 (uz + Uy) - u = 1
Transcribed Image Text:SITUATION 1 Classify the following PDES as either elliptic, parabolic, or hyperbolic. Notation: • u, = first partial derivative of u(x, y) with respect to x %3D = first partial derivative of u(x, y) with respect to y • Uy • Uux = second partial derivative of u(x, y) with respect to x = second partial derivative of u(x, y) with respect to y %3D Uyy Uxy = second partial derivative of u(x, y) with respect to x and y • Ugy = Uyx %3D Uzz + 5 (uz + Uy) - u = 1
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