Jyotisolanki at 12:02, 27 March 2017

2017-03-27T12:02:29Z

Jyotisolanki at 05:12, 8 February 2016

2016-02-08T05:12:38Z

Jyotisolanki at 11:22, 28 December 2015

2015-12-28T11:22:31Z

Jyotisolanki: 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''' |- | 00:0..."

2015-12-28T09:19:28Z

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''' |- | 00:0..."

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 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

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| 00:33
| '''Ubuntu 12.04''' as the operating system

|-
| 00:36
|and '''Scilab 5.3.3''' version.

|-
|00:40
|To practice 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 parenthesis '''y zero, t zero, t''' and '''f'''.

|-

|01:10

|| Here '''y zero''' is the initial condition 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 of 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 summarizes 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 242: / Line 242: @@
 | 03:47
-| જો તમે  '''y,'''  ની વેલ્યુ જોવ્ક ઈચ્છો છો તો કન્સોલ પર ટાઈપ કરો '''y''' અને એન્ટર દબાવો.
+| જો તમે  '''y,'''  ની વેલ્યુ જોવા ઈચ્છો છો તો કન્સોલ પર ટાઈપ કરો '''y''' અને એન્ટર દબાવો.
 |-
@@ Line 248: / Line 248: @@
 | 03:54
-| '''y''' અને  '''y dash''' ની વેલ્યુ દ્રશ્યમાન છે.
+|  અને  '''y dash''' ની વેલ્યુ દ્રશ્યમાન છે.
 |-
@@ Line 346: / Line 346: @@
 | 05:41
-|  '''voltage વિરુદ્ધ time''' is shown.  '''voltage વિરુદ્ધ time''' નો પ્લોટ દેખાય છે.
+|  '''voltage વિરુદ્ધ time''' નો પ્લોટ દેખાય છે.
 |-

@@ Line 19: / Line 19: @@
 |-
 |00:12
-|*  '''Scilab ode function''' ને વાપરતા
+|  '''Scilab ode function''' ને વાપરતા
 |-
 |00:15
-|*  '''ODEs''' ના વિશિષ્ટ ઉદાહરણને હલ કરવું અને
+|  '''ODEs''' ના વિશિષ્ટ ઉદાહરણને હલ કરવું અને
 |-
 | 00:18
-|* સોલ્યુશનને કેવી રીતે પ્લોટ કરાવાય.
+| સોલ્યુશનને કેવી રીતે પ્લોટ કરાવાય.
 |-
@@ Line 35: / Line 35: @@
 |-
 | 00:24
-|*  '''simple pendulum''' ની ગતિ.
+|  '''simple pendulum''' ની ગતિ.
 |-
 | 00:26
-|* '''Van der Pol equation'''
+| '''Van der Pol equation'''
 |-
 |00:28
-|* અને  ''' Lorenz system'''.
+| અને  ''' Lorenz system'''.
 |-

Scilab/C4/ODE-Applications/Gujarati - Revision history

Jyotisolanki at 12:02, 27 March 2017

Jyotisolanki at 05:12, 8 February 2016

Jyotisolanki at 11:22, 28 December 2015

Jyotisolanki: 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''' |- | 00:0..."