Difference between revisions of "Scilab/C4/ODE-Euler-methods/English-timed"

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| Welcome to the Spoken Tutorial on '''“Solving ODEs using Euler Methods” '''
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| Welcome to the Spoken Tutorial on '''Solving ODEs using Euler Methods'''.
  
 
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|-
 
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|00:18
 
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|Develop '''Scilab''' code to solve '''ODEs'''
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|Develop '''Scilab''' code to solve '''ODEs'''.
  
 
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|00:25
 
|00:25
 
|'''Ubuntu 12.04''' as the operating system  
 
|'''Ubuntu 12.04''' as the operating system  
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|-
 
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| 00:28
 
| 00:28
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|and '''Scilab 5.3.3''' version  
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|and '''Scilab 5.3.3''' version.
  
 
|-
 
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| 00:32
 
| 00:32
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| To practise this tutorial, a learner  
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| To practice this tutorial, a learner  
  
 
|-
 
|-
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|'''y dash is equal to minus two t minus y.'''  
 
|'''y dash is equal to minus two t minus y.'''  
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|-
 
|-
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|| and the '''step length''' is given as '''zero point one.'''  
 
|| and the '''step length''' is given as '''zero point one.'''  
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|-
 
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|01:36
 
|01:36
 
|Let us look at the code for '''Euler method.'''  
 
|Let us look at the code for '''Euler method.'''  
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|-
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||We define the function '''Euler underscore o d e with arguments f, t init, y init, h and n'''
 
||We define the function '''Euler underscore o d e with arguments f, t init, y init, h and n'''
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|-
 
|-
 
|01:58
 
|01:58
 
|'where '''f''' denotes the function to be solved,  
 
|'where '''f''' denotes the function to be solved,  
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|-
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|02:05
 
|02:05
  
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||'''y init'''  is the initial value of '''y'''
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||'''y init'''  is the initial value of '''y''',
 
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|-
  
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| 02:42
 
| 02:42
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|Save and execute the file '''Euler underscore o d e dot sci'''
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|'''Save and execute''' the file '''Euler underscore o d e dot sci'''
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+
  
 
|-
 
|-
 
| 02:49
 
| 02:49
 
|Switch to '''Scilab console''' to solve the example problem.  
 
|Switch to '''Scilab console''' to solve the example problem.  
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−
 
  
 
|-
 
|-
 
| 02:54
 
| 02:54
 
|We define the ''' function ''' by typing  
 
|We define the ''' function ''' by typing  
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|-
 
|-
 
| 02:56
 
| 02:56
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|'''d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to open paranthesis minus two asterisk t close paranthesis minus y close single quote close paranthesis '''
+
|'''d e f f open parenthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to open parenthesis minus two asterisk t close parenthesis minus y close single quote close parenthesis '''
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+
  
 
|-
 
|-
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|-
 
|-
 
|03:28
 
|03:28
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| Then type '''t init is equal to zero. '''
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| Then type: '''t init is equal to zero. '''
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+
  
 
|-
 
|-
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| 03:31
 
| 03:31
  
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|Press '''Enter. '''
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|Press '''Enter.'''
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+
−
 
+
−
 
+
  
 
|-
 
|-
  
 
| 03:33
 
| 03:33
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||Type '''y init is equal to minus one. '''
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||Type: '''y init is equal to minus one.'''
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'
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−
 
+
  
 
|-
 
|-
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|03:38
 
|03:38
  
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||Press '''Enter '''
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||Press '''Enter '''.
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+
  
 
|-
 
|-
  
 
| 03:40
 
| 03:40
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| Type '''step length h is equal to zero point one. '''
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| Type: '''step length h is equal to zero point one.'''
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+
−
 
+
  
 
|-
 
|-
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| 03:44
 
| 03:44
  
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| Press '''Enter'''
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| Press '''Enter'''.
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+
  
 
|-
 
|-
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| The '''step length is zero point one,''' and we have to find the value of '''y''' at '''zero point five.'''
 
| The '''step length is zero point one,''' and we have to find the value of '''y''' at '''zero point five.'''
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|-
 
|-
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||So, the number of '''iterations''' should be '''five.'''  
 
||So, the number of '''iterations''' should be '''five.'''  
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|-
 
|-
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|At each '''iteration,'''  the value of '''t''' will be increased by '''zero point one.'''  
 
|At each '''iteration,'''  the value of '''t''' will be increased by '''zero point one.'''  
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|-
 
|-
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| 04:05
 
| 04:05
  
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| So type '''capital N is equal to five.'''  
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| So type '''capital N is equal to five'''  
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+
−
 
+
−
 
+
  
 
|-
 
|-
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| 04:09
 
| 04:09
  
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|And press '''Enter.'''
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|and press '''Enter.'''
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+
  
 
|-
 
|-
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| 04:11
 
| 04:11
  
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| To '''call''' the '''function,''' type  
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| To '''call''' the '''function,''' type:
  
 
|-
 
|-
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| 04:14
 
| 04:14
  
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| '''open square bracket t comma y close square bracket equal to Euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis '''
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| '''open square bracket t comma y close square bracket equal to Euler underscore o d e open parenthesis f comma t init comma y init comma h comma capital N close parenthesis '''
  
 
|-
 
|-
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||Press '''Enter.'''  
 
||Press '''Enter.'''  
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|-
 
|-
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|It is a '''second order method''' and is a '''stable two step method. '''
 
|It is a '''second order method''' and is a '''stable two step method. '''
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|-
 
|-
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|We find the '''average''' of the '''function''' at the beginning and end of '''time step.'''  
 
|We find the '''average''' of the '''function''' at the beginning and end of '''time step.'''  
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|-
 
|-
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|Let us solve this example using '''Modified Euler method.'''  
 
|Let us solve this example using '''Modified Euler method.'''  
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|-
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|We are given a '''function y dash is equal to t plus y plus t y. '''
 
|We are given a '''function y dash is equal to t plus y plus t y. '''
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−
 
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|-
 
|-
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|We have to find the value of '''y'''  at '''time t equal to zero point one ''' using '''Modified Euler's method.'''  
 
|We have to find the value of '''y'''  at '''time t equal to zero point one ''' using '''Modified Euler's method.'''  
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|-
 
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| 05:25
 
| 05:25
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| Let us look at the code for '''Modified Euler method on Scilab Editor'''
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| Let us look at the code for '''Modified Euler method''' on '''Scilab Editor'''.
  
 
|-
 
|-
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| 05:39
 
| 05:39
  
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| '''where f''' is the '''function''' to be solved
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| where: '''f''' is the '''function''' to be solved,
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+
  
 
|-
 
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| 05:45
 
| 05:45
  
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| '''y init''' is the inital value of  '''y'''
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| '''y init''' is the inital value of  '''y''',
  
 
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|-
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| '''h''' is the '''step length''' and  
 
| '''h''' is the '''step length''' and  
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|We implement '''Modified Euler Method''' here.  
 
|We implement '''Modified Euler Method''' here.  
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|Save and execute the file '''Modi Euler underscore o d e dot sci.'''  
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|'''Save and execute''' the file '''Modi Euler underscore o d e dot sci.'''  
 
|-
 
|-
  
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|Press '''Enter.'''  
 
|Press '''Enter.'''  
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|-
 
|-
  
 
| 06:32
 
| 06:32
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|Define the '''function''' by typing '''d e f f open paranthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to t plus y plus t asterisk y close single quote close paranthesis'''  
+
|Define the '''function''' by typing '''d e f f open parenthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to t plus y plus t asterisk y close single quote close parenthesis'''  
  
 
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|-
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|Press '''Enter.'''
 
|Press '''Enter.'''
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|-
 
|-
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| 07:03
 
| 07:03
  
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|Then type '''t init equal to zero''',  press Enter  
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|Then type: '''t init equal to zero''',  press Enter.
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+
  
 
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| 07:08
  
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|Type '''y init equal to one''' and press '''Enter.'''  
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|Type: '''y init equal to one''' and press '''Enter.'''  
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+
  
 
|-
 
|-
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| 07:12
 
| 07:12
  
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|Then type '''h equal to zero point zero one''' press '''Enter.'''  
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|Then type: '''h equal to zero point zero one''' press '''Enter.'''  
  
 
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| 07:19
 
| 07:19
  
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|Type '''capital N equal to ten.'''  
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|Type: '''capital N equal to ten.'''  
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+
  
 
|-
 
|-
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| 07:36
 
| 07:36
  
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|Then call the '''function modi euler underscore o d e''' by typing.'''
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|Then call the '''function modi euler underscore o d e''' by typing:
  
 
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| 07:41
  
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|'''open square bracket t comma y close square bracket equal to modi euler underscore o d e open paranthesis f comma t init comma y init comma h comma capital N close paranthesis'''  
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|'''open square bracket t comma y close square bracket equal to modi euler underscore o d e open parenthesis f comma t init comma y init comma h comma capital N close parenthesis'''  
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+
  
 
|-
 
|-
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|Press '''Enter. '''
 
|Press '''Enter. '''
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|-
 
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|We have also learnt to solve '''ODEs''' using these methods in '''Scilab.'''  
 
|We have also learnt to solve '''ODEs''' using these methods in '''Scilab.'''  
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|-
 
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|08:28
 
|08:28
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| Watch the video available at the  link shown below
+
| Watch the video available at the  link shown below.
  
 
|-
 
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| 08:32
 
| 08:32
  
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| It summarises the Spoken Tutorial project  
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| It summarizes the Spoken Tutorial project.
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+
−
 
+
  
 
|-
 
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|08:35
 
|08:35
  
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||If you do not have good bandwidth, you can download and watch it  
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||If you do not have good bandwidth, you can download and watch it.
  
 
|-
 
|-
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|08:40
 
|08:40
  
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||The spoken tutorial project Team
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||The spoken tutorial project Team:
  
 
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|08:42
 
|08:42
  
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||Conducts workshops using spoken tutorials  
+
||Conducts workshops using spoken tutorials.
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+
  
 
|-
 
|-
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|08:45
 
|08:45
  
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||Gives certificates to those who pass an online test  
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||Gives certificates to those who pass an online test.
−
 
+
  
 
|-
 
|-
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|08:49
 
|08:49
  
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||For more details, please write to contact@spoken-tutorial.org  
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||For more details, please write to contact@spoken-tutorial.org.
−
 
+
  
 
|-
 
|-
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|08:55
 
|08:55
  
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|Spoken Tutorial Project is a part of the Talk to a Teacher project  
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|Spoken Tutorial Project is a part of the Talk to a Teacher project.
−
 
+
−
 
+
  
 
|-
 
|-
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| 09:07
 
| 09:07
  
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|More information on this mission is available at the link shown below
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|More information on this mission is available at the link shown below.
  
 
|-
 
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| 09:13
 
| 09:13
  
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|This is Ashwini Patil signing off.
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|This is Ashwini Patil, signing off.
  
 
|-
 
|-

Revision as of 18:10, 2 March 2015

Time Narration
00:01 Dear Friends,
00:02 Welcome to the Spoken Tutorial on Solving ODEs using Euler Methods.
00:09 At the end of this tutorial, you will learn how to:
00:12 Solve ODEs using Euler and Modified Euler methods in Scilab
00:18 Develop Scilab code to solve ODEs.
00:22 To record this tutorial, I am using
00:25 Ubuntu 12.04 as the operating system
00:28 and Scilab 5.3.3 version.
00:32 To practice this tutorial, a learner
00:34 should have basic knowledge of Scilab
00:37 and should know how to solve ODEs.
00:40 To learn Scilab, please refer to the relevant tutorials available on the Spoken Tutorial website.
00:48 In Euler method, we get an accurately approximate solution of the ODE.
00:55 It is used to solve initial value problems where initial values of the differential equation are given.
01:03 It can be used to solve continuous functions.
01:08 Let us solve an example using Euler method.
01:12 We are given an initial value problem -
01:15 y dash is equal to minus two t minus y.
01:20 The initial value of y is given as minus one
01:25 and the step length is given as zero point one.
01:29 We have to find the value of y at time t equal to zero point five.
01:36 Let us look at the code for Euler method.
01:39 Open Euler underscore o d e dot sci on Scilab editor.
01:47


We define the function Euler underscore o d e with arguments f, t init, y init, h and n
01:58 'where f denotes the function to be solved,
02:01 t init is the initial value of time t,
02:05 y init is the initial value of y,
02:09 h is the step length, and n is the number of iterations.
02:14 Then we initialize the values of t and y to vectors of zeros.
02:21 We place the initial values of t and y in t of one and y of one respectively.
02:29 Then we iterate from one to N to find the value of y.
02:33 Here we apply Euler method to find the value of y.
02:39 Finally we end the function.
02:42 Save and execute the file Euler underscore o d e dot sci
02:49 Switch to Scilab console to solve the example problem.
02:54 We define the function by typing
02:56 d e f f open parenthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to open parenthesis minus two asterisk t close parenthesis minus y close single quote close parenthesis
03:26 Press Enter.
03:28 Then type: t init is equal to zero.
03:31 Press Enter.
03:33 Type: y init is equal to minus one.
03:38 Press Enter .
03:40 Type: step length h is equal to zero point one.
03:44 Press Enter.
03:46 The step length is zero point one, and we have to find the value of y at zero point five.
03:53 So, the number of iterations should be five.
03:59 At each iteration, the value of t will be increased by zero point one.
04:05 So type capital N is equal to five
04:09 and press Enter.
04:11 To call the function, type:
04:14 open square bracket t comma y close square bracket equal to Euler underscore o d e open parenthesis f comma t init comma y init comma h comma capital N close parenthesis
04:33 Press Enter.
04:35 The value of y at t equal to zero point five is shown.
04:41 Now let us look at Modified Euler method.
04:45 It is a second order method and is a stable two step method.
04:51 We find the average of the function at the beginning and end of time step.
04:56 Let us solve this example using Modified Euler method.
05:02 We are given a function y dash is equal to t plus y plus t y.
05:08 The initial value of y is one
05:12 and the step length is zero point zero one.
05:16 We have to find the value of y at time t equal to zero point one using Modified Euler's method.
05:25 Let us look at the code for Modified Euler method on Scilab Editor.
05:31 We define the function with arguments f, t init, y init, h and n
05:39 where: f is the function to be solved,
05:42 t init is the intial time value,
05:45 y init is the inital value of y,
05:49 h is the step length and
05:51 n is the number of iterations.
05:54 Then we initialize the arrays for y and t.
05:58 We place the initial values of t and y in t of one and y of one respectively.
06:07 We implement Modified Euler Method here.
06:11 Here we find the average value of y at the beginning and end of time step.
06:17 Save and execute the file Modi Euler underscore o d e dot sci.
06:23 Switch to Scilab console.
06:26 Clear the screen by typing c l c.
06:30 Press Enter.
06:32 Define the function by typing d e f f open parenthesis open single quote open square bracket y dot close square bracket equal to f of t comma y close single quote comma open single quote y dot equal to t plus y plus t asterisk y close single quote close parenthesis
07:01 Press Enter.
07:03 Then type: t init equal to zero, press Enter.
07:08 Type: y init equal to one and press Enter.
07:12 Then type: h equal to zero point zero one press Enter.
07:19 Type: capital N equal to ten.
07:22 Since the number of iterations should be ten to time t equal to zero point one with step length of zero point zero one.
07:34 Press Enter.
07:36 Then call the function modi euler underscore o d e by typing:
07:41 open square bracket t comma y close square bracket equal to modi euler underscore o d e open parenthesis f comma t init comma y init comma h comma capital N close parenthesis
08:03 Press Enter.
08:05 The value of y at t equal to zero point one is shown.
08:10 Let us summarize this tutorial.
08:14 In this tutorial we have learnt to develop Scilab code for Euler and modified Euler methods.
08:21 We have also learnt to solve ODEs using these methods in Scilab.
08:28 Watch the video available at the link shown below.
08:32 It summarizes the Spoken Tutorial project.
08:35 If you do not have good bandwidth, you can download and watch it.
08:40 The spoken tutorial project Team:
08:42 Conducts workshops using spoken tutorials.
08:45 Gives certificates to those who pass an online test.
08:49 For more details, please write to contact@spoken-tutorial.org.
08:55 Spoken Tutorial Project is a part of the Talk to a Teacher project.
09:00 It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
09:07 More information on this mission is available at the link shown below.
09:13 This is Ashwini Patil, signing off.
09:15 Thank you for joining.

Contributors and Content Editors

Gaurav, PoojaMoolya, Sandhya.np14

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