NUMERICAL METHODS - All questions tutorial 1 & 2-tutorial 3 - Q1-6 only!!- do not attempt any...

Question

NUMERICAL METHODS
- All questions tutorial 1 & 2
-tutorial 3 - Q1-6 only!!
- do not attempt any second order differential equations using 4th order runge kutta method.
MATRICES
- TUTORIAL 1 , Q 1) - A,D,G - ONLY! Q3 And Q4
- TUT2 - Q1,Q2,Q3(A) , Q4,Q5,Q6
- TUT3 - Q1,Q2,Q3,Q4

005_heme8zk-hh00uuji.zip 005_qeme8zk-es2qaodb.zip 005_juqe8zk-ur3wifh2.docx

David · Accepted Answer

 
 
 
 
 
 
 
2
2
2
1
1
2
2
2
2
2
0 0 0
1 1
1 0 1 0 0 0
# 2
, ,
, ,
, ,
, ,
0, 1, 0
1. '
.2
, ,
0
, ,
n n
TUTORIAL
d y dy
y x
dx dx
dy
let z f x y z
dx
f x y z z
dz
then z y x
dx
dz
x z y f x y z
dx
f x y z x z y
x y z given
euler s method
nowtake h
y y hf x y z
n
y y hf x y z

  
 

  
   
  
  

 

 
 
 
 
 
1
1 0 1 0 0 0
1
1 .2* 0,1,0
1 .2*0 1
.1
0
, ,
1 .1* 0,1,0 1
f
ans
now takeh
n
y y hf x y z
f
 
  


 
  
 
 
 
 
 
 
 
1 2
1 0 2 0 0 0
1
2
2 1 1 1 1 1
1
, ,
, ,
0 .1* 0,1,0
0 .1* 0 1 0 .1
1
, ,
1 .1* .1,1, .1
1 .1*.1
.99
n n n n nz z hf x y z
z z hf x y z
f
n
y y hf x y z
f
ans
  
 
 
     

 
  
 


 
 
 
 
 
 
 
 
 
 
11 1 0 0 0
1
21 2
2 2
12 1 0 0 11 0 21
1
1
22 2 0 0 11 0 21
2
1
2 sec .
.2 0
, ,
0,1,0
0
0,1,0
0 1 0 1
, ,
.2,1 .2*0,0 .2* 1
.2,1, .2
.2
, ,
.2,1 .2*0,0 .2* 1
.2,1, .2
.
ond order R K method
h n
k f x y z
f
k f
x y z
k f x h y hk z hk
f
f
k f x h y hk z hk
f
f
 




       
   
   
 
 
   
   
 

 
2
1 0 11 12
2 1 .2 .6
.2
2
.2
1 * .2
2
.98
y y k k
ans
   
  
  

 
Part b  Now h=.1 
 
 
 
 
 
 
11 1 0 0 0
1
21 2
2 2
12 1 0 0 11 0 21
1
1
0
, ,
0,1,0
0
0,1,0
0 1 0 1
, ,
.1,1 .1*0,0 .1* 1
.1,1, .1
.1
n
k f x y z
f
k f
x y z
k f x h y hk z hk
f
f





       
   
   
 
 

 
 
 
 
 
 
 
 
 
 
22 2 0 0 11 0 21
2
1
2
1 0 11 12
1 0 21 22
11 1 1 1 1
1
21 2
, ,
.1,1 .1*0,0 .1* 1
.1,1, .1
.1 1 .1 .8
.1
2
.1
1 * 0 .1
2
.995
.1
2
.

NUMERICAL METHODS - All questions tutorial 1 & 2 -tutorial 3 - Q1-6 only!! - do not attempt any second order differential equations using 4th order runge kutta method. MATRICES - TUTORIAL 1 , Q 1) -...

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