Scilab/C4/ODE-Applications/English-timed - Revision history

PoojaMoolya at 05:41, 10 March 2017

2017-03-10T05:41:41Z

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Sandhya.np14 at 05:51, 3 March 2015

2015-03-03T05:51:06Z

Sandhya.np14 at 05:49, 3 March 2015

2015-03-03T05:49:29Z

Sandhya.np14 at 05:47, 3 March 2015

2015-03-03T05:47:56Z

Sandhya.np14 at 04:45, 3 March 2015

2015-03-03T04:45:11Z

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Gaurav at 11:13, 3 September 2014

2014-09-03T11:13:48Z

Gaurav at 05:09, 11 July 2014

2014-07-11T05:09:42Z

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PoojaMoolya: Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the Spoken Tutorial on '''“Solving ODEs using Scilab ode Function”''' |- | 00.09 | A…'

2014-03-13T09:00:32Z

Created page with '{| Border=1 || Time || Narration |- | 00.01 |Dear Friends, |- | 00.02 | Welcome to the Spoken Tutorial on '''“Solving ODEs using Scilab ode Function”''' |- | 00.09 | A…'

New page

{| Border=1

|| Time

|| Narration

|-
| 00.01
|Dear Friends,

|-
| 00.02
| Welcome to the Spoken Tutorial on '''“Solving ODEs using Scilab ode Function”'''

|-
| 00.09
| At the end of this tutorial, you will learn how to:

|-
|00.12
|'''Use Scilab ode function'''

|-
|00.15
|Solve typical examples of '''ODEs''' and

|-
| 00.18
|Plot the solution

|-
|00.21
|The typical examples we will be

|-
| 00.24
|Motion of '''simple pendulum'''

|-
| 00.26
|'''Van der Pol equation'''

|-
|00.28
|and ''' Lorenz system'''

|-
|00.30
|To record this tutorial, I am using

|-
| 00.33
| '''Ubuntu 12.04''' as the operating system

|-
| 00.36
|and '''Scilab 5.3.3''' version

|-
|00.40
|To practise this tutorial, a learner should have basic knowledge of '''Scilab'''

|-

|00.45

|and should know how to solve '''ODEs.'''

|-

|00.48
|To learn '''Scilab,''' please refer to the relevant tutorials available on the '''Spoken Tutorial''' website.

|-

| 00.56

|The '''ode function''' is an '''ordinary differential equation solver.'''

|-

| 01.01
||The syntax is '''y equal to ode within paranthesis y zero, t zero, t and f'''

|-

|01.10

|| Here '''y zero''' is the initial conditon of the '''ODEs'''

|-

|01.15

| '''t zero''' is the '''initial time'''

|-
|01.17
|'''t''' is the '''time range'''

|-

|01.19

|and '''f''' is the '''function'''

|-

|01.22

||Consider the motion of '''simple pendulum.'''

|-
|01.25
|Let '''theta t''' be the angle made by the '''pendulum''' with the '''vertical''' at time '''t.'''

|-

| 01.33
|We are given the initial conditions

|-

|01.36

|'''theta zero''' is equal to '''pi by four''' and

|-

|01.39

| '''theta dash of zero''' is equal to '''zero.'''

|-

|01.44

| Then the position of the '''pendulum''' is given by
|-

| 01.47

|| '''theta double dash t minus g by l into sin of theta t equal to zero.'''

|-
| 01.56
| Here '''g equal to 9.8 m per second square''' is the '''acceleration due to gravity''' and

|-
|02.03
|''' l equal to zero point five meter''' is the '''length''' of the '''pendulum.'''

|-
|02.11
| For the given initial conditions, we have to solve the '''ODE''' within the '''time range zero less than equal to t less than equal to five.'''

|-
| 02.22
|We also have to '''plot''' the solution.

|-
| 02.25
|Let us look at the code for solving this problem.

|-
| 02.29
|Open '''pendulum dot sci''' on '''Scilab editor.'''

|-
| 02.34
|The first line of the code defines the initial conditions of the '''ODE.'''

|-
|02.40
|Then we define the intial time value. And we provide the '''time range.'''

|-
|02.46
| Next, we convert the given equation to a system of '''first order ODEs.'''

|-

| 02.52

|We substitute the values of '''g''' and '''l''' .

|-

| 02.56
||Here we take '''y''' to be the given '''variable theta''' and '''y dash''' to be '''theta dash.'''
'

|-

|03.03

|Then we call the '''ode function''' with '''arguments y zero, t zero, t''' and the '''function Pendulum.'''

|-

| 03.12
| The solution to the '''equation''' will be a '''matrix''' with two '''rows.'''

|-

| 03.17

| The first '''row''' will contain the values of '''y''' in the given '''time range.'''

|-

| 03.21

| The second '''row''' will contain the values of '''y dash ''' within the '''time range. '''

|-

|03.27

|Hence we plot both the '''rows''' with respect to '''time. '''

|-

|03.31

|Save and execute the file '''Pendulum dot sci'''

|-

| 03.37

|The plot shows how the values of '''y''' and '''y dash''' vary with '''time. '''

|-

| 03.44

|Switch to '''Scilab console'''

|-

| 03.47

| If you want to see the values of '''y,''' type '''y''' on the '''console''' and press '''Enter.'''

|-

| 03.54

|The values of '''y''' and '''y dash''' are displayed.
|-

| 03.58

|Let us solve '''Van der Pol equation''' using the '''ode function.'''

|-

| 04.03

|We are given the '''equation '''

|-

| 04.06

|'''v double dash of t plus epsilon into v of t square minus one into v dash of t plus v of t equal to zero.'''

|-

| 04.20

|The initial '''conditions''' are '''v of two equal to one''' and '''v dash of two equal to zero. '''

|-

| 04.28

|Assume '''epsilon is equal to zero point eight nine seven. '''

|-

|04.32

|We have to find the solution within the '''time range two less than t less than ten and then plot''' the solution.

|-

| 04.42

|Let us look at the code for '''Van der Pol equation. '''

|-

| 04.47

| Switch to '''Scilab editor''' and open '''vander pol dot sci.'''

|-

| 04.53

| We define the initial conditions of the '''ODEs''' and '''time''' and then define the '''time range. '''

|-

| 05.01

|Since the '''inital time value''' is given as '''two''', we start the time range at two.

|-
| 05.07
| Then we define the '''function vander pol''' and construct a system of '''first order ODEs.'''

|-
| 05.15
|We substitute the value of '''epsilon''' with '''zero point eight nine seven. '''

|-

| 05.21

|Here '''y''' refers to the '''voltage v.'''

|-

| 05.25

| Then we call '''ode function''' and solve the system of '''equations.'''

|-

| 05.30

| Finally we plot '''y''' and '''y dash versus t.'''

|-

| 05.35

| Save and execute the file '''vander pol dot sci.'''

|-

| 05.41

|The '''plot''' showing '''voltage versus time''' is shown.

|-

| 05.45

|Let's move onto '''Lorenz system of equations.'''

|-

| 05.50

|The '''Lorenz system of equations''' is given by

|-

| 05.53

|'''x one dash equal to sigma into x two minus x one, '''

|-

| 06.00

|'''x two dash equal to one plus r minus x three into x one minus x two and '''

|-

| 06.08

|'''x three dash equal to x one into x two minus b into x three.'''

|-

| 06.16

|The initial conditions are '''x one zero''' equal to '''minus ten, x two zero''' equal to '''ten''' and '''x three zero''' equal to '''twenty five.'''

|-

| 06.29

|Let '''sigma''' be equal to '''ten, r''' be equal to '''twenty eight and b''' equal to '''eight by three.'''

|-

| 06.37

|Switch to '''Scilab editor''' and open '''Lorenz dot sci'''

|-

| 06.44
|We start by defining the initial conditions of the '''ODEs.'''

|-

| 06.48

|Since there are three different '''ODEs,''' there are three initial conditions.

|-

| 06.54

|Then we define the '''inital time''' condition and next the '''time range.'''

|-

| 07.00

|We define the '''function Lorenz''' and then define the given constants '''sigma, r and b.'''

|-

| 07.08

|Then we define the '''first order ODEs. '''

|-

| 07.12

|Then we call the '''ode function''' to solve the '''Lorenz system of equations.'''

|-

| 07.18

|We equate the solution to '''x.'''

|-

| 07.21

|Then we '''plot x one, x two''' and '''x three versus time. '''

|-

| 07.28

|Save and execute the file '''Lorenz dot sci.'''

|-

| 07.33

|The '''plot''' of '''x one, x two''' and '''x three versus time''' is shown.

|-

| 07.39

|Let us summarize this tutorial.

|-

| 07.41

|In this tutorial we have learnt to develop '''Scilab code''' to solve an '''ODE''' using '''Scilab ode function.'''

|-

| 07.50

|Then we have learnt to '''plot''' the solution.

|-
|07.53
| Watch the video available at the link shown below

|-

| 07.56

| It summarises the Spoken Tutorial project

|-

|07.59

||If you do not have good bandwidth, you can download and watch it

|-

|08.04

||The spoken tutorial project Team

|-

|08.06

||Conducts workshops using spoken tutorials

|-

|08.09

||Gives certificates to those who pass an online test

|-

|08.13

||For more details, please write to contact@spoken-tutorial.org

|-

|08.20

|Spoken Tutorial Project is a part of the Talk to a Teacher project

|-

| 08.23

| It is supported by the National Mission on Eduction through ICT, MHRD, Government of India.
|-

| 08.31

|More information on this mission is available at the link shown below

|-

| 08.36

|This is Ashwini Patil signing off.

|-

|08.38

| Thank you for joining.

@@ Line 87: / Line 87: @@
 |01:10
-|| Here '''y zero''' is the initial conditions of the '''ODEs''',
+|| Here '''y zero''' is the initial condition of the '''ODEs''',
 |-

@@ Line 19: / Line 19: @@
 |-
 |00:12
-|'''Use Scilab ode function'''
+|* Use Scilab ode function
 |-
 |00:15
-|Solve typical examples of '''ODEs''' and
+|* Solve typical examples of '''ODEs''' and
 |-
 | 00:18
-|Plot the solution.
+|* Plot the solution.
 |-

@@ Line 11: / Line 11: @@
 |-
 | 00:02
-| Welcome to the Spoken Tutorial on '''Solving ODEs using Scilab ode Function'''
+| Welcome to the Spoken Tutorial on '''Solving ODEs using Scilab ode function'''
 |-
@@ Line 76: / Line 76: @@
 | 00:56
-|The '''ode''' function is an '''ordinary differential equation''' solver.
+|The '''ode''' function is an '''ordinary differential equation solver'''.
 |-
@@ Line 87: / Line 87: @@
 |01:10
-|| Here '''y zero''' is the initial condition of the '''ODEs''',
+|| Here '''y zero''' is the initial conditions of the '''ODEs''',
 |-
@@ Line 124: / Line 124: @@
 |01:36
-|'''theta zero''' is equal to '''pi by four''' and
+|'''theta of zero''' is equal to '''pi by four''' and
 |-
@@ Line 149: / Line 149: @@
 |-
 |02:03
-|''' l equal to zero point five meter''' is the '''length''' of the '''pendulum.'''
+|''' l equal to zero point five meter''' is the length of the '''pendulum.'''
 |-
@@ Line 165: / Line 165: @@
 |-
 | 02:29
-|Open '''pendulum dot sci''' on '''Scilab editor.'''
+|Open '''Pendulum dot sci''' on '''Scilab editor.'''
 |-
@@ Line 194: / Line 194: @@
 |03:03
-|Then we call the '''ode function''' with '''arguments y zero, t zero, t''' and the '''function Pendulum.'''
+|Then we call the '''ode''' function with arguments '''y zero, t zero, t''' and the function '''Pendulum.'''
 |-
 | 03:12
-| The solution to the '''equation''' will be a '''matrix''' with two '''rows.'''
+| The solution to the equation will be a '''matrix''' with two '''rows.'''
 |-
@@ Line 252: / Line 252: @@
 | 03:58
-|Let us solve '''Van der Pol equation''' using the '''ode function.'''
+|Let us solve '''Van der Pol equation''' using the '''ode''' function.
 |-
@@ Line 270: / Line 270: @@
 | 04:20
-|The initial '''conditions''' are '''v of two equal to one''' and '''v dash of two equal to zero. '''
+|The initial conditions are '''v of two equal to one''' and '''v dash of two equal to zero. '''
 |-
@@ Line 294: / Line 294: @@
 | 04:47
-| Switch to '''Scilab editor''' and open '''vander pol dot sci.'''
+| Switch to '''Scilab editor''' and open '''Vander pol dot sci.'''
 |-
@@ Line 310: / Line 310: @@
 |-
 | 05:07
-| Then we define the '''function vander pol''' and construct a system of '''first order ODEs.'''
+| Then we define the '''function Vander pol''' and construct a system of '''first order ODEs.'''
 |-
@@ Line 326: / Line 326: @@
 | 05:25
-| Then we call '''ode function''' and solve the system of '''equations.'''
+| Then we call '''ode''' function and solve the system of '''equations.'''
 |-
@@ Line 338: / Line 338: @@
 | 05:35
-| Save and execute the file '''vander pol dot sci.'''
+| Save and execute the file '''Vander pol dot sci.'''
 |-
@@ Line 380: / Line 380: @@
 | 06:16
-|The initial conditions are '''x one zero''' equal to '''minus ten,  x two zero''' equal to '''ten''' and '''x three zero''' equal to '''twenty five.'''
+|The initial conditions are '''x one zero  equal to minus ten''',  '''x two zero equal to ten''' and '''x three zero equal to twenty five.'''
 |-
@@ Line 386: / Line 386: @@
 | 06:29
-|Let '''sigma''' be equal to '''ten,  r''' be equal to '''twenty eight and b''' equal to '''eight by three.'''
+|Let '''sigma''' be equal to '''ten,  r''' be equal to '''twenty eight''' and '''b''' equal to '''eight by three.'''
 |-
@@ Line 415: / Line 415: @@
 | 07:00
-|We define the '''function Lorenz''' and then define the given constants '''sigma, r and b.'''
+|We define the '''function Lorenz''' and then define the given constants '''sigma, r''' and '''b.'''
 |-
@@ Line 427: / Line 427: @@
 | 07:12
-|Then we call the '''ode function''' to solve the '''Lorenz system of equations.'''
+|Then we call the '''ode''' function to solve the '''Lorenz system of equations.'''
 |-

← Older revision		Revision as of 11:13, 3 September 2014
Line 207:		Line 207:
	\| 02:56		\| 02:56
	\|\|Here we take '''y''' to be the given '''variable theta''' and '''y dash''' to be '''theta dash.'''		\|\|Here we take '''y''' to be the given '''variable theta''' and '''y dash''' to be '''theta dash.'''
−	'	+