Tutorial questions: Chapter 5 EX1. Determine the types of the following PDEs
(a) (b) Ans.
T 2T =k 2 t x
2T 2T + =0 2x 2 y
(a) Parabolic PDE.
(b) Elliptic PDE
2u = 2u 2u 2u + + 2x 2 y 2z
EX2. Calcula
ME4906 Revision Questions (Part II)
Chapter 5 1. 2. 3. 4. 5. 6. How is partial differentiation defined? EX2 of tutorial questions Give an example for parabolic and elliptic PDEs respectively. EX1 of t
Chapter 6 Finite-Element Method
Finite element method (FEM) provides an alternative to finite-difference (FD) methods, especially for systems with irregular geometry, unusual boundary conditions, or
Lecture Notes
ME4906, Mechanical Engineering, PolyU
2008/2009
5.3.2 Implicit Scheme
It has been shown that numerical instability occurs due to the explicit scheme. An implicit scheme is constructed as
Solution: 1. (a)
22 22 T = sin(nx ) e 4 n t [4n 2 2 ] = 4n 2 2 sin(nx ) e 4n t t
(b)
22 22 T = cos(nx ) [n ] e 4 n t = n cos(nx ) e 4 n t x 22 2T T = ( ) = [n cos(nx ) e 4 n t ] x x 2 x x
= n 2 2 sin(
Lecture Notes
ME4906, Mechanical Engineering, PolyU
2008/2009
5.3 Finite Difference for PDE of 1D in Space
5.3.1 Explicit Scheme
Consider the problem of 1D unsteady heat transfer defined below,
T 2T =
Chapter 5.3
Finite Difference for PDE of 1D in Space
Parabolic equations are employed to characterize time-variable (unsteady-state) problems. Conservation of energy can be used to develop an unstead
Solution to Class Test held on 4 March 2009
1. (a) B
1
= max(17, 21, 15) = 21,
B
= max(10, 6, 37) = 37.
(b) Using the given value B 1
= 2/7, we have
cond (B, ) = B
B 1
= 37 (2/7) = 74/7.
The system is
Tutorial questions: Chapter 5 EX1. Determine the types of the following PDEs
(a) (b) Ans.
T 2T =k 2 t x
2T 2T + =0 2x 2 y
(a) Parabolic PDE.
(b) Elliptic PDE
2u = 2 u 2u 2u + + 2 x 2 y 2z
EX2. Calcu
Lab Report (ME4906)
Student Name_
Student ID _
1. Calculate the first derivative and its absolute error of
f ( x) = sin x x3
at x=4 using the forward 2nd-order finite difference scheme with intervals
Lecture Notes
ME4906, Mechanical Engineering, PolyU
2008/2009
Chapter 5 Partial Differential Equations and Finite Difference Methods
5.2 PDE of 1D Heat Transfer Problem
5.2.1 Governing Equation and An
Assignment #1 ME4906 Numerical Methods for Product Analysis (Deadline for submission: 01 April 2009, 10:00pm)
(Mar 18, 2009)
1. The temperature T of a rod depends on time (t) and position (x) and can
SUBJECT DESCRIPTION
_ Subject Title :
Numerical Methods for Product Analysis
Instructor: Dr. G. P. Zheng, Department of Mechanical Engineering, Hong Kong PolyU. (E-mail): [email protected], (Tel):