PoojaMoolya at 05:46, 10 March 2017

2017-03-10T05:46:07Z

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Sandhya.np14 at 16:20, 2 March 2015

2015-03-02T16:20:06Z

Sandhya.np14 at 12:41, 2 March 2015

2015-03-02T12:41:33Z

Sandhya.np14 at 12:40, 2 March 2015

2015-03-02T12:40:23Z

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Gaurav at 05:00, 11 July 2014

2014-07-11T05:00:38Z

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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 Euler Methods” ''' |- | 00.09 | At the …'

2014-03-13T05:54:23Z

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

New page

{| Border=1

|| 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

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|00.25
|'''Ubuntu 12.04''' as the operating system

|-
| 00.28
|and '''Scilab 5.3.3''' version

|-
| 00.32
| To practise 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'''

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|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''',

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|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'''.

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|02.33
| Here we apply '''Euler method''' to find the value of '''y. '''

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|02.39
| Finally we end the '''function. '''

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| 02.42
|Save and execute the file '''Euler underscore o d e dot sci'''

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| 02.49
|Switch to '''Scilab console''' to solve the example problem.

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| 02.54
|We define the ''' function ''' by typing

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| 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 '''

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|03.26
|Press '''Enter. '''

|-
|03.28
| Then type '''t init is equal to zero. '''

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| 03.31

|Press '''Enter. '''

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| 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.'''

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|03.59

|At each '''iteration,''' the value of '''t''' will be increased by '''zero point one.'''

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| 04.05

| So type '''capital N is equal to five.'''

|-

| 04.09

|And press '''Enter.'''

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| 04.11

| To '''call''' the '''function,''' type

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| 04.14

| '''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

||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. '''

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| 04.45

|It is a '''second order method''' and is a '''stable two step method. '''

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| 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.'''

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| 05.02

|We are given a '''function y dash is equal to t plus y plus t y. '''

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| 05.08

| The initial value of '''y''' is '''one'''

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| 05.12

| and the '''step length''' is '''zero point zero one.'''

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| 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,

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| 05.45

| '''y init''' is the inital value of '''y'''

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| 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.'''
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| 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.

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| 06.11

|Here we find the average value of '''y''' at the beginning and end of '''time step.'''

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| 06.17

|Save and execute the file '''Modi Euler underscore o d e dot sci.'''
|-

| 06.23

|Switch to '''Scilab console.'''

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| 06.26

|Clear the screen by typing '''c l c.'''
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| 06.30

|Press '''Enter.'''

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| 06.32
|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'''

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| 07.01

|Press '''Enter.'''

|-

| 07.03

|Then type '''t init equal to zero''', press Enter

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| 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 paranthesis f comma t init comma y init comma h comma capital N close paranthesis'''

|-

| 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.

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| 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 summarises 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.

@@ Line 84: / Line 84: @@
 | 01:20
-||The initial value of y is given as '''minus one'''
+||The initial value of y is given as '''minus one'''(-1)
 |-
@@ Line 90: / Line 90: @@
 |01:25
-|| and the '''step length''' is given as '''zero point one.'''
+|| and the '''step length''' is given as '''zero point one'''(0.1).
 |-
@@ Line 112: / Line 112: @@
 |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,
 |-
@@ Line 132: / Line 132: @@
 |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.'''
 |-
@@ Line 138: / Line 138: @@
 |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.'''
 |-
@@ Line 155: / Line 155: @@
 |-
 |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 213: / Line 213: @@
 | 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.'''
 |-
@@ Line 231: / Line 231: @@
 | 04:05
-| So type '''capital N is equal to five'''
+| So type capital '''N is equal to five''' (N=5)
 |-
@@ Line 317: / Line 317: @@
 |-
 | 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'''
 |-
@@ Line 346: / Line 346: @@
 | 05:51
-| '''n''' is the number of '''iterations.'''
+| '''N''' is the number of '''iterations.'''
 |-
@@ Line 426: / Line 426: @@
 | 07:19
-|Type: '''capital N equal to ten.'''
+|Type: capital '''N equal to ten'''
 |-
@@ Line 432: / Line 432: @@
 | 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.'''
 |-
@@ Line 444: / Line 444: @@
 | 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:
 |-
@@ Line 450: / Line 450: @@
 | 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'''
 |-

← Older revision		Revision as of 12:41, 2 March 2015
Line 111:		Line 111:

	\|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'''

Scilab/C4/ODE-Euler-methods/English-timed - Revision history

PoojaMoolya at 05:46, 10 March 2017

Sandhya.np14 at 16:20, 2 March 2015

Sandhya.np14 at 12:41, 2 March 2015

Sandhya.np14 at 12:40, 2 March 2015

Gaurav at 05:00, 11 July 2014

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