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

Latest revision as of 11:16, 10 March 2017

Time	Narration
00:01	Dear Friends, 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(-1)
01:25	and the step length is given as zero point one(0.1).
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 (N=5)
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

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

Latest revision as of 11:16, 10 March 2017

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@@ Line 1: / Line 1: @@
 {| Border=1
-|| Time
+|'''Time'''
+|'''Narration'''
-|| Narration
 |-
-| 00.01
+| 00:01
-|Dear Friends,
+|Dear Friends,  Welcome to the Spoken Tutorial on '''Solving ODEs using Euler Methods'''.
 |-
-| 00.02
+| 00:09
-| 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
+|00:12
 |Solve '''ODEs''' using '''Euler''' and '''Modified Euler methods''' in '''Scilab'''
 |-
-|00.18
+|00:18
-|Develop '''Scilab''' code to solve '''ODEs'''
+|Develop '''Scilab''' code to solve '''ODEs'''.
 |-
-| 00.22
+| 00:22
 |To record this tutorial, I am using
 |-
-|00.25
+|00:25
 |'''Ubuntu 12.04''' as the operating system
 |-
-| 00.28
+| 00:28
-|and '''Scilab 5.3.3''' version
+|and '''Scilab 5.3.3''' version.
 |-
-| 00.32
+| 00:32
-| To practise this tutorial, a learner
+| To practice this tutorial, a learner
 |-
-|00.34
+|00:34
 |should have basic knowledge of '''Scilab'''
 |-
-|00.37
+|00:37
 |and should know how to solve '''ODEs.'''
 |-
-| 00.40
+| 00:40
 | To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.
 |-
-| 00.48
+| 00:48
 | In '''Euler method,''' we get an accurately approximate solution of the '''ODE.'''
 |-
-|00.55
+|00:55
 |It is used to solve initial value problems where initial values of the '''differential equation''' are given.
 |-
-|01.03
+|01:03
 | It can be used to solve '''continuous functions.'''
 |-
+|01:08
-|01.08
 |Let us solve an example using '''Euler method.'''
 |-
+|01:12
-|01.12
 |We are given an initial value problem -
 |-
+| 01:15
-| 01.15
 |'''y dash is equal to minus two t minus y.'''
 |-
+| 01:20
-| 01.20
+||The initial value of y is given as '''minus one'''(-1)
-||The initial value of y is given as '''minus one'''
 |-
+|01:25
-|01.25
+|| and the '''step length''' is given as '''zero point one'''(0.1).
-|| and the '''step length''' is given as '''zero point one.'''
 |-
+|01:29
-|01.29
 | We have to find the value of '''y''' at time '''t equal to zero point five.'''
 |-
-|01.36
+|01:36
 |Let us look at the code for '''Euler method.'''
 |-
+|01:39
-|01.39
 |Open '''Euler underscore o d e dot sci''' on '''Scilab editor.'''
 |-
+|01:47
-|01.47
+||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'''
 |-
-|01.58
+|01:58
-|'where '''f''' denotes the function to be solved,
+|'where: '''f''' denotes the function to be solved,
 |-
+| 02:01
-| 02.01
 |'''t init''' is the initial value of time '''t''',
 |-
+|02:05
-|02.05
+||'''y init'''  is the initial value of '''y''',
-||'''y init'''  is the initial value of '''y'''
 |-
+|02:09
-|02.09
+| '''h''' is the '''step length''' and '''n''' is the number of '''iterations.'''
-| '''h''' is the '''step length,''' and '''n''' is the number of '''iterations.'''
 |-
+|02:14
-|02.14
+| Then we initialize the values of '''t''' and '''y''' to vectors of '''zeros.'''
-| Then we initialize the values of '''t''' and '''y to vectors of zeros. '''
 |-
+| 02:21
-| 02.21
 || We place the initial values of '''t''' and '''y''' in '''t of one''' and '''y of one''' respectively.
 |-
-| 02.29
+| 02:29
 | Then we '''iterate''' from '''one to N''' to find the value of '''y'''.
 |-
-|02.33
+|02:33
 | Here we apply '''Euler method''' to find the value of '''y. '''
 |-
-|02.39
+|02:39
-| Finally we end the '''function. '''
+| Finally we '''end''' the '''function.'''
 |-
-| 02.42
+| 02:42
-|Save and execute the file '''Euler underscore o d e dot sci'''
+|'''Save and execute''' the file '''Euler underscore o d e dot sci'''.
 |-
-| 02.49
+| 02:49
 |Switch to '''Scilab console''' to solve the example problem.
 |-
-| 02.54
+| 02:54
 |We define the ''' function ''' by typing
 |-
-| 02.56
+| 02:56
-|'''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 '''
 |-
-|03.26
+|03:26
 |Press '''Enter. '''
 |-
-|03.28
+|03:28
-| Then type '''t init is equal to zero. '''
+| Then type: '''t init is equal to zero. '''
 |-
+| 03:31
-| 03.31
+|Press '''Enter.'''
-|Press '''Enter. '''
 |-
+| 03:33
-| 03.33
+||Type: '''y init is equal to minus one.'''
-||Type '''y init is equal to minus one.  '''
-'
 |-
+|03:38
-|03.38
+||Press '''Enter '''.
-||Press '''Enter '''
 |-
+| 03:40
-| 03.40
+| Type: '''step length h is equal to zero point one.'''
-| Type '''step length h is equal to zero point one. '''
 |-
+| 03:44
-| 03.44
+| Press '''Enter'''.
-| Press '''Enter'''
 |-
+| 03:46
-| 03.46
+| 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.'''
 |-
+|03:53
-|03.53
 ||So, the number of '''iterations''' should be '''five.'''
 |-
+|03:59
-|03.59
 |At each '''iteration,'''  the value of '''t''' will be increased by '''zero point one.'''
 |-
+| 04:05
-| 04.05
+| So type capital '''N is equal to five''' (N=5)
-| So type '''capital N is equal to five.'''
 |-
+| 04:09
-| 04.09
+|and press '''Enter.'''
-|And press '''Enter.'''
 |-
+| 04:11
-| 04.11
+| To '''call''' the '''function,''' type:
-| To '''call''' the '''function,''' type
 |-
+| 04:14
-| 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 '''
-| '''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 '''
 |-
+| 04:33
-| 04.33
 ||Press '''Enter.'''
 |-
+| 04:35
-| 04.35
 ||The value of '''y at t equal to zero point five''' is shown.
 |-
+| 04:41
-| 04.41
 ||Now let us look at '''Modified Euler method. '''
 |-
+| 04:45
-| 04.45
 |It is a '''second order method''' and is a '''stable two step method. '''
 |-
+| 04:51
-| 04.51
 |We find the '''average''' of the '''function''' at the beginning and end of '''time step.'''
 |-
+|04:56
-|04.56
 |Let us solve this example using '''Modified Euler method.'''
 |-
+| 05:02
-| 05.02
 |We are given a '''function y dash is equal to t plus y plus t y. '''
 |-
+| 05:08
-| 05.08
 | The initial value of '''y''' is '''one'''
 |-
+| 05:12
-| 05.12
 | and the '''step length''' is '''zero point zero one.'''
 |-
+| 05:16
-| 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
+| 05:25
-| Let us look at the code for '''Modified Euler method on Scilab Editor'''
+| Let us look at the code for '''Modified Euler method''' on '''Scilab Editor'''.
 |-
-| 05.31
+| 05:31
-|We define the '''function''' with '''arguments f, t init, y init, h and n'''
+|We define the '''function''' with '''arguments f, t init, y init, h''' and '''n'''
 |-
+| 05:39
-| 05.39
+| where: '''f''' is the '''function''' to be solved,
-| '''where f''' is the '''function''' to be solved
 |-
+| 05:42
-| 05.42
 | '''t init''' is the intial '''time''' value,
 |-
+| 05:45
-| 05.45
+| '''y init''' is the inital value of  '''y''',
-| '''y init''' is the inital value of  '''y'''
 |-
+| 05:49
-| 05.49
 | '''h''' is the '''step length''' and
 |-
+| 05:51
-| 05.51
+| '''N''' is the number of '''iterations.'''
-| '''n''' is the number of '''iterations.'''
 |-
+| 05:54
-| 05.54
 | Then we initialize the '''arrays''' for '''y''' and '''t.'''
 |-
+| 05:58
-| 05.58
 |We place the initial values of '''t''' and '''y''' in '''t of one''' and '''y of one''' respectively.
 |-
+| 06:07
-| 06.07
 |We implement '''Modified Euler Method''' here.
 |-
+| 06:11
-| 06.11
 |Here we find the average value of '''y''' at the beginning and end of '''time step.'''
 |-
+| 06:17
-| 06.17
+|'''Save and execute''' the file '''Modi Euler underscore o d e dot sci.'''
-|Save and execute the file '''Modi Euler underscore o d e dot sci.'''
 |-
+| 06:23
-| 06.23
 |Switch to '''Scilab console.'''
 |-
+| 06:26
-| 06.26
 |Clear the screen by typing '''c l c.'''
 |-
+| 06:30
-| 06.30
 |Press '''Enter.'''
 |-
+| 06:32
-| 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'''
-|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'''
 |-
+| 07:01
-| 07.01
 |Press '''Enter.'''
 |-
+| 07:03
-| 07.03
+|Then type: '''t init equal to zero''',  press Enter.
-|Then type '''t init equal to zero''',  press Enter
 |-
+| 07:08
-| 07.08
+|Type: '''y init equal to one''' and press '''Enter.'''
-|Type '''y init equal to one''' and press '''Enter.'''
 |-
+| 07:12
-| 07.12
+|Then type: '''h equal to zero point zero one''' press '''Enter.'''
-|Then type '''h equal to zero point zero one''' press '''Enter.'''
 |-
+| 07:19
-| 07.19
+|Type: capital '''N equal to ten'''
-|Type '''capital N equal to ten.'''
 |-
+| 07:22
-| 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.'''
-|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
-| 07.34
 |Press '''Enter.'''
 |-
+| 07:36
-| 07.36
+|Then call the '''function Modi Euler underscore o d e''' by typing:
-|Then call the '''function modi euler underscore o d e''' by typing.'''
 |-
+| 07:41
-| 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'''
-|'''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'''
 |-
+| 08:03
-| 08.03
 |Press '''Enter. '''
 |-
+| 08:05
-| 08.05
 |The value of '''y at t equal to zero point one''' is shown.
 |-
+| 08:10
-| 08.10
 |Let us summarize this tutorial.
 |-
+| 08:14
-| 08.14
 |In this tutorial we have learnt to develop Scilab code for '''Euler''' and '''modified Euler methods.'''
 |-
+| 08:21
-| 08.21
 |We have also learnt to solve '''ODEs''' using these methods in '''Scilab.'''
 |-
-|08.28
+|08:28
-| Watch the video available at the  link shown below
+| Watch the video available at the  link shown below.
 |-
+| 08:32
-| 08.32
+| It summarizes the Spoken Tutorial project.
-| It summarises the Spoken Tutorial project
 |-
+|08:35
-|08.35
+||If you do not have good bandwidth, you can download and watch it.
-||If you do not have good bandwidth, you can download and watch it
 |-
+|08:40
-|08.40
+||The spoken tutorial project Team:
-||The spoken tutorial project Team
 |-
+|08:42
-|08.42
+||Conducts workshops using spoken tutorials.
-||Conducts workshops using spoken tutorials
 |-
+|08:45
-|08.45
+||Gives certificates to those who pass an online test.
-||Gives certificates to those who pass an online test
 |-
+|08:49
-|08.49
+||For more details, please write to contact@spoken-tutorial.org.
-||For more details, please write to contact@spoken-tutorial.org
 |-
+|08:55
-|08.55
+|Spoken Tutorial Project is a part of the Talk to a Teacher project.
-|Spoken Tutorial Project is a part of the Talk to a Teacher project
 |-
+| 09:00
-| 09.00
 | It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
 |-
+| 09:07
-| 09.07
+|More information on this mission is available at the link shown below.
-|More information on this mission is available at the link shown below
 |-
+| 09:13
-| 09.13
+|This is Ashwini Patil, signing off.
-|This is Ashwini Patil signing off.
 |-
+|09:15
-|09.15
 | Thank you for joining.