Chapter 08.05: Lesson: Higher Order and Coupled ODEs: Euler's Method Example: Part 1 of 2

[@saddamal-hammadi9550]

Thanks for you effort, I barely found an explanation for solving higher order differential equation numerically. I really appreciate your work.

[@ConstantinSchieber]

This video did help me alot with those problems. Keep up the good work - many students will thank you!

[@zachburt9507]

Great example. Explained very clearly!

[@numericalmethodsguy]

Thank you. To get even more help, subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods

[@TheDesertFox84]

Thanks for explaining! Better than the books :D

[@rajanalexander4949]

Thank you for this. This is really helpful and clear!

[@numericalmethodsguy]

Thank you. Please subscribe and ask your friends to subscribe - our goal is to get to 100,000 subscribers by the end of 2021. To get even more help, subscribe to the numericalmethodsguy channel kzbin.info, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources. Follow the numerical methods blog at AutarKaw.org. You can also take a free massive open online course (MOOC) at canvas.instructure.com/enroll/KYGTJR Please share these links with your friends and fellow students through social media and email. Support the channel if you able to do so at kzbin.info/store

[@shelley-anneharrisberg7409]

Thanks very much! Wonderful clear explanation - it helped a lot!

[@digitizerSF]

Did you do a video on modified Euler's Method, Professor??? I'd love to see one.

[@holgus103]

Thank you, a very helpful video.

[@numericalmethodsguy]

Thank you. To get even more help, subscribe to the numericalmethodsguy channel, and go to MathForCollege.com/nm and MathForCollege.com/ma for more resources and share the link with your friends through social media and email. Support the site by buying the textbooks at www.lulu.com/shop/search.ep?keyWords=autar+kaw&type= Follow my numerical methods blog at AutarKaw.org. You can also take a free online course at www.canvas.net/?query=numerical%20methods

[@BBeaRRable]

Nice and clear. Like it :)

[@Swucken]

Thanks, helped a lot!

[@christophermartinez3844]

How would one calculate the error analysis for a 2nd order problem under this method?

[@BiswajitRoy-gp3fx]

How z=dy/dx is written as a function of (x,y,z)

[@numericalmethodsguy]

It is written as 0*x+0*y+1*z. dy/dx value is same as z; but z is dependent on y (z=dy/dx) and y is dependent on x, so dy/dx is a function of x,y,z. Keep in mind, x is the only independent variable here, z is an introduced dependent variable and y is the dependent variable of the ODE.

[@537Davis]

Thank u sir

[@fsp3328]

LIFE SAVER

[@easyphysicstutorials8713]

Sir please provide me a numerical method for solving 2nd order differential equation (if the equation has a singularity).

[@nhungtran-oi7ow]

Thank you so much!!!

[@burtonkorten9322]

Perfect

[@RajevSVelu]

Is this the modified Euler's Method Professor???

[@isaachiew4906]

how is f1(0, 7, 13) = 13?

[@numericalmethodsguy]

f1(xi,yi,zi)=zi; so f1(0,7,13)=13

[@fightingwithghosts]

thank you

[@engsam2208]

thank u so much..i need sheet paper or book for high order 3rd... i needmore examples ... plz i wish you can help me

[@abhaygshah]

awesome!

[@numericalmethodsguy]

No, this is not modified Euler's method!

[@aniszouaoui4740]

hay i have a quetion if they don't give you h how can you find the results for example dy(t)/dt=(t+1)^2+y ; f(0.1)=0.105 at t=0.2 Exct solution find y(0.2)=?????

[@numericalmethodsguy]

Your problem is posed improperly. What is f, did you mean y. You cannot find exact value using numerical methods. You can definitely do this by using exact methods like Laplace transforms. If you are asked to do this numerically, choose an h=0.05 as (0.2-0.1)/h gives no remainder. You can choose any other h value also where (0.2-0.1)/h does not leave a remainder. Then keep halving the h value till the absolute relative approximate is less than some pre-specified tolerance. The value of y(0.2) you will get will be a numerical value that is not exact though!

[@aniszouaoui4740]

thank you very very much this problem was asked in a doctors exame enters from last year

[@jophia90]

you are so awesomeeee! :DDD

[@suneeshk1508]

Nice

[@luischil]

Yesss :D

[@lashelawrence1273]

Wahala dey😭😂