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# Partial Differential Equations - PowerPoint PPT Presentation

Partial Differential Equations. Chapter 12 Burden and Faires. General 2 nd Order Form. Discriminant. Classification. Conic Sections. Classification. Elliptical PDE. Elliptical PDE. FDM Molecule. ODE Second Order Formula. x i+1. x i. x i-1.

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## PowerPoint Slideshow about ' Partial Differential Equations' - gema

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### Partial Differential Equations

Chapter 12

Burden and Faires

PDE's

General 2nd Order Form

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

xi+1

xi

xi-1

PDE's

Consider a square plate 0.5 m on a side. Two sides are held at 0o and two sides vary from 0 to 100o

PDE's

PDE's

4

3

2

1

j = 0

i = 0 1 2 3 4

PDE's

y4

y3

y2

y1

y0

x0 x1 x2 x3 x4

PDE's

y4

y3

y2

y1

y0

x0 x1 x2 x3 x4

PDE's

PDE's

PDE's

• For smaller systems use a direct method.

• Gaussian Elimination

• Matrix Factorization

• For larger systems use an iterative method.

• Gauss-Seidel

• Successive Over Relaxation

PDE's

PDE's

PDE's

PDE's

N

W

E

S

PDE's

• Alternative Solution Techniques.

• Derivative B.C.

• Nonuniform Boundaries.

• Alternative Coordinate systems.

PDE's

Alternating Direct Implicit Method

PDE's

Alternating Direct Implicit Method

PDE's

12

0

12

PDE's

PDE's

PDE's

PDE's

PDE's

Alternating Direct Implicit Method- Rows

PDE's

Alternating Direct Implicit Method- Columns

PDE's

• Function value specified on boundary are called Dirichlet B.C.

• Derivative values specified on boundary are called Neumann Boundary Conditions

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

4 equations in 6 unknowns.

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's

PDE's