By Majid khan

fx

u

2

2

Parabolic

1. Conduction of heat in bars and solids

2. Diffusion of concentration of liquid or gaseous substance in physical chemistry

3. Diffusion of vorticity in viscous fluid flow

4. Slow motion in hydrodynamics5. Telegraph transmission in cables of

low inductance or capacitance etc

Example

Using (FDM)Solve the 1D poission boundary value problem,

0101,02

2

uuinfx

u

One-dimensional mesh

2xonApproxmatidifferenceCentral

condtionsboundaryDirichletuu

Nifx

uuu

N

iii

0

...2,12

0

211

1.Homogeneous Dirichlet-Neumann BC

(2) Non-homogeneous Dirichlet BC

(3).Non-homogeneous Neumann BC

(4) Non-homogenous Robin BC

Thank you