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

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(Created page with "{| Border=1 |'''Time''' |'''Narration''' |- | 00:01 |નમસ્તે મિત્રો, |- | 00:02 | ''' Euler Methods''' નો ઉપયોગ કરીને ODEs...")
 
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| In '''Euler method,''' માં આપણને '''ODE.''' ના હલ નું we get an accurately approximate solution of the '''ODE.'''................में, हमें 'ODE' के हल का ठीक अनुमान मिलता है। 
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| In '''Euler method,''' માં આપણને '''ODE.''' ના હલ નું we get an accurately approximate solution of the '''ODE.'''................
  
 
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|00:55
 
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|It is used to solve initial value problems where initial values of the '''differential equation''' are given.  
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| આ ઇનીશીયલ વેલ્યુ પ્રોબ્લમસ ને હલ કરવા માટે ઉપયોગી છે જ્યાં '''differential equation''' ની ઇનીશીયલ વેલ્યુ આપેલ હોય છે.
  
 
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|01:03
 
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| It can be used to solve '''continuous functions.'''  
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| આ '''continuous functions.''' ને હલ કરવા માટે ઉપયોગી છે.
  
 
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|Let us solve an example using '''Euler method.'''
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| '''Euler method.''' ચાલો '''Euler method.'''  મેથડ વાપરીને ઉદાહરણને હલ કરીએ.
  
 
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|We are given an initial value problem -
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| આપણને એક ઇનીશીયલ વેલ્યુ પ્રોબ્લમ આપેલ છે.
  
 
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||The initial value of y is given as '''minus one'''(-1)  
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|| '''y'''  ઇનીશીયલ વેલ્યુ  '''minus one'''(-1) આપેલી છે.
  
 
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|| and the '''step length''' is given as '''zero point one'''(0.1).  
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|| અને  '''step length''' '''zero point one'''(0.1) આપેલ છે.  
  
 
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| We have to find the value of '''y''' at time '''t equal to zero point five.'''  
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| આપણને ટાઈમ '''t equal to zero point five.''' પર '''y'''  ની વેલ્યુ શોધવાની છે.
  
 
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|01:36
 
|01:36
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|Let us look at the code for '''Euler method.'''  
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| હવે '''Euler method.''' ના માટે કોડ જોઈએ.
 
   
 
   
 
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|Open '''Euler underscore o d e dot sci''' on '''Scilab editor.'''
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| '''Scilab editor.''' પર 'Euler underscore o d e dot sci''' ખોલો.
  
 
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Revision as of 15:27, 29 December 2015

Time Narration
00:01 નમસ્તે મિત્રો,
00:02 Euler Methods નો ઉપયોગ કરીને ODEs હલ કરવા પરના પોકન ટ્યુટોરિયલમાં તમારું સ્વાગત છે.
00:09 આ ટ્યુટોરીયલ ના અંતે તમે શીખશો કેવી રીતે:
00:12 Scilab' માં Euler અને Modified Euler methods વાપરીને ODEs હલ કરતા.
00:18 ODEs હલ કરવા માટે Scilab કોડ બનાવતા.
00:22 આ ટ્યુટોરિયલ રિકોર્ડ કરવા માટે હું ઉપયોગ કરી રહી છું,
00:25 Scilab 5.3.3 વર્જન સાથે .
00:28 Ubuntu 12.04 ઓપરેટીંગ સીસ્ટમ
00:32 આ ટ્યુટોરિયલ ના અભ્યાસ માટે તમને
00:34 Scilab નું સમાન્ય જ્ઞાન હોવું જોઈએ.
00:37 અને ODEs. ને કેવી રીતે હલ કરાય તેની જાણ હોવી જોઈએ.
00:40 સાઈલેબ ને શીખવા માટે સ્પોકન ટ્યુટોરિયલ વેબ સાઈટ પર સાઈલેબ પર ઉપલબ્ધ સંબંધિત ટ્યુટોરિયલ જુઓ.
00:48 In Euler method, માં આપણને ODE. ના હલ નું we get an accurately approximate solution of the ODE.................
00:55 આ ઇનીશીયલ વેલ્યુ પ્રોબ્લમસ ને હલ કરવા માટે ઉપયોગી છે જ્યાં differential equation ની ઇનીશીયલ વેલ્યુ આપેલ હોય છે.
01:03 આ continuous functions. ને હલ કરવા માટે ઉપયોગી છે.
01:08 Euler method. ચાલો Euler method. મેથડ વાપરીને ઉદાહરણને હલ કરીએ.
01:12 આપણને એક ઇનીશીયલ વેલ્યુ પ્રોબ્લમ આપેલ છે.
01:15 y dash is equal to minus two t minus y.
01:20 y ઇનીશીયલ વેલ્યુ minus one(-1) આપેલી છે.
01:25 અને step length zero point one(0.1) આપેલ છે.
01:29 આપણને ટાઈમ t equal to zero point five. પર y ની વેલ્યુ શોધવાની છે.
01:36 હવે Euler method. ના માટે કોડ જોઈએ.
01:39 Scilab editor. પર 'Euler underscore o d e dot sci ખોલો.
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.

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