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

Contributors and Content Editors

Navigation menu

Personal tools

Namespaces

Variants

Views

Actions

Search

Navigation

Tools

@@ Line 6: / Line 6: @@
 |-
 | 00:01
-|Dear Friends,
+|Dear Friends,  Welcome to the Spoken Tutorial on '''Solving ODEs using Euler Methods'''.
-|-
-| 00:02
-| Welcome to the Spoken Tutorial on '''Solving ODEs using Euler Methods'''.
 |-
@@ Line 65: / Line 61: @@
 |-
 |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'''
+||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).
-|| 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.'''
@@ Line 103: / Line 89: @@
 |-
 |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'''
-||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,
+|'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.'''
-| '''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.'''
-| 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.
@@ Line 155: / Line 128: @@
 |-
 |02:39
-| Finally we end the '''function. '''
+| Finally we '''end''' the '''function.'''
 |-
 | 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'''.
 |-
@@ Line 182: / Line 155: @@
 |-
 | 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.'''
-| 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)
-| 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.'''
@@ Line 317: / Line 248: @@
 |-
 | 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
 | 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.'''
-| '''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'''
-|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.'''
-|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:
-|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'''
-|'''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.'''
@@ Line 487: / Line 363: @@
 |-
 | 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.