Runge Kutta Method Easily Explained + Trick on Casio fx-991ES Calculator!

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Playlist of all my Numerical Methods videos-

Today I'll tell you how to solve First Order Ordinary Differential Equations by Runge-Kutta Method of 4th Order. Also,how to do the calculations easily using Casio fx-991ES Calculator.

Topics explained in this video-
1. Understanding First Order Differential Equation question
2. What's the meaning of dy/dx and function of xy
3. How to calculate K1,K2,K3,K4 for 4th Order Runge-Kutta Method,with detailed explanation in each step
4. How to remember Runge-Kutta Method formula
5. What is interval of differencing or h
6. How to calculate y1 or the value of Y for given value of X

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I've uploaded videos on Statistics,Numerical Methods,
Business & Financial Mathematics,Operation Research,Computer Science & Engineering(CSE),Android Application Reviews,India Travel & Tourism,Street Foods,Life Tips and many other topics.

And a series of videos showing how to use your scientific calculators Casio fx-991ES & fx-82MS to do maths easily.

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Комментарии

This video has no tricks, just plain substitutions. :3

onkarphatak

Hi Sujoy. This was a great video. I did an additional calculation. I calculated the error of approximation between the exact solution and the approximate solution at x=1.2. In order to do that I had to calculate the exact solution of the differential equation by solving the equation analytically. I used separation of variables.
y´=yx
y´/y=x
Integral (y’/y)=integral (x)
ln(y) = (1/2)x^2+c
e^(ln(y))=e^( (1/2)x^2+c )
y=e^( (1/2)x^2+c )
y=e^( (1/2)x^2 ) e^c
y=e^(0.5x^2) k
y=k e^(0.5x^2)
The initial condition was y(1)=2, so calculated k
2= k e^( 0.5(1)^2 )
2=ke^0.5
k=2/e^0.5
k=2e^(-0.5)
So, the exact solution is:
y=2e^(-0.5) e^(0.5x^2)
The exact value at x = 1.2 is
y_exact=2e^(-0.5) e^(0.5(1.2)^2)
y_exact=2.49215
According to the video the approximate value was:
Y_approx= 2.49214
The error of approximation at x= 1.2 is
error = | y_exact-y_approx | = |2.49215-2.49214|= 0.00001
I am a graduate student of specialization in electric power systems at Universidad Central de Venezuela in Caracas. Best regards from Venezuela.

CarlosDominguez-yric

Thanks Brother....
Ur explanation was very easy💯
Wish me luck...today is my M3 😜

shrivatsadeshpande

Thnku So much! Your Lessons saved my life! Subscribed!

NaveenKumar-sfql

THANKS SUJOY BHAI I'M REALLY IMPRESS WITH U
NOW U CAN SAY I'M FAN OF U
ALL VIDEOS ARE VERY VERY HELPFUL FOR MY EXAM

AbhishekSingh-rvrt

thanks brother, best method of understanding the RK Method

MuhammadWaseem-pgzn

I am still understood no dought about that method no confusion sir thanku ..

meenameena

thank you sir ! your all videos are helpful !

merajkhan

There are no tricks same formula is used and it's normal usage of calculator

maazosmany

Your understanding method is good sir thank you sir

sky

Thank you sir, well explained the topic.very helpful video

wingsofwords

You are the best man! Thank you a lot!

offroaderOO

this was much helpful, it was clearly understable thank a lot, ,,,

Hearit

All your videos are soo good, thanks a lot sir.

jayasreeajs

Thank you Mr.Sujoy..I had adoubt regarding this...Actually our faculty has taught this method in whole different way.They did by Iteration in a tabular form.So which one is more accurate according to you sir..??

SurajBonthapuri