Euler's Method: Example

[JuliusDuthoy]

Very helpful. Thanks for the video.

[neekoz]

3:45 pretty sure 5+2=7... is that just me?

[numericalmethodsguy]

@neekoz There is an annotation on the video: 5+(1)3=8

[exteam12]

it is easy

[thekendokid]

what a fantastic explanation!

[wangbungal]

what is the difference with this and a modified euler method?

[rohailahmedhashmi]

Thnx Teach , Appreciate your efforts ;)

[hellosaila]

i learned from watching these videos than from going to class for 5 weeks.

[freazeezy]

if dy/dx=(y+2)^2+4 and y(at step 0)=y(0)=0. how do you use eulers method to find y at step 1? h=0.1

[lmfdjtiko]

1:24 - 1:28 made me LOL

[numericalmethodsguy]

@lmfdjtiko What made you LOL. I can use a laugh today even if it is at my expense!

[punchpuneeth]

@numericalmethodsguy I think why he LOL'd was because @ 1:24 it sound like this, "When I choose h = 3, owlbe there are 3 ppl to be then equal to get what the value y equal to 3 :D" you said that really fast that made it funny :)

[Njzavitz]

@numericalmethodsguy Listen to how fast he says it all

[tenacious1884]

@Njzavitz you forgot that 'he' is the guy who you are replying to. lol

he teaches and he answers comments!

[discipleofknowledge]

If there is no 'x' in the original equation, do we just use x=0? For example, y'=y y(0)=1. When we are doing euler's method for y1 or y2, do we use x=0 in the part of the equation that says F(x,y)?

[numericalmethodsguy]

@discipleofknowledge No, you use 0*x, for your example, y'=y would be rewritten as y'=y+0*x. Sometimes this is needed to be done in some programming languages where they expect x as well as y term in f(x,y).

[Soumilbharatendu]

Sir,

i just wanted to ask is that why do we keep h fixed we could change it's value after each iteration(like after i=0,i=1,...so on) ?

[numericalmethodsguy]

@Soumilbharatendu Yes, you can change h after each step (it is not called iteration as it is not refining a value). But how would one decide on the value of h for next step. h is kept constant for programming purposes. There are "adaptive" routines which change h. Do a search on - adaptive step size Euler - and you will see some references.

[jayproduction01]

Picard is better to solve ODE!!!!!

[subs367]

Nice to see videos like this on YouTube. Thank you.

[707monty]

Dr. You saved me in my mid1 and then again in midterm 2 and tomarow is my final exam and i know i would b among the top students again :) coz my youtube teacher is the best :))

[impulsepainter]

Very much appreciated. Understand Euler's Method much better now.

[flyfalcon91]

I need Help i have to use Euler's Method to find a National Debt. The trick is that im only given the Years, Revenues and outlay. Im given 18 years from 1939 to 1991 but not every year is included. im also given the Revenues for the years and the outlay. How can i use Euler's Method to find the National Debt?

[spacelover1000]

good n easy explanation ..thank u sir..very easy method

[xxxyzabcde1]

Can u describe euler's modified method pls?

[spacelover1000]

@xxxyzabcde1 hellow ..modified euler method s very simple than tis one..tat s...y(n+1)=y(n)+hF{x(n)+h/2,y(­n)+h/2f(x(n),y(n))}.........fo­llow the same procedure what you used in euler method.

[pegadirty]

Beautiful. I'm going to use this as a framework for my C++ program on Euler's method, which I think is going to be much easier than I thought.

Thank you very much Doctor!

[robinsingh1111]

Thanks a lot, helped a lot.

[LeYenHuong]

Thank you so much for the way you explain. So easy to follow and understand

[ceslopez86]

Interesting!! But there's something I cannot understand entirely in this method, how do I calculate the True Value?

[numericalmethodsguy]

@ceslopez86 You would use analytical techniques. Go to numericalmethods(dot)end(dot)u­sf(dot)edu and click on Primer on ODEs. See the Youtube videos there!

[ceslopez86]

@numericalmethodsguy Thanks a lot for your help!!!

[numericalmethodsguy]

@ceslopez86 See another exact solution method: Go to autarkaw(dot)wordpress(dot)com and go to the calendar on the right. Look for the entry made on January 7, 2011 of "Example: Solving First Order Linear ODE by Integrating Factor"

[ceslopez86]

@numericalmethodsguy Thank you so much :)

[enk010]

You can compute it using separable equation, la place inverse, integrating factor, it depends on ODE a good referral website is Pauls online note.

[navyseai]

once more you lesson helped me remembering what i forgot :P thanks

[mr1madmonkey]

fantastic video, saved me from screwing myself over on the midterm. thanks a lot dude

[bernardengks]

Thanks. You are just an awesome dude.

[nomadicme]

you are amazing! Much much much better than my lecturer!

[MechEngineering45]

In the future, could you provide a tutorial for implicit Euler ? Also, perhaps talk about how they can be used for solving stiff ODE's.

[phatcow27]

WOW! this was SO much more clear than this silly handout i got on euler's method! this really helped me finish my mathematica lab on time... is there a point when making the value of "h" so smaller and smaller eventually has negligible effect on approximating the accuracy?

[numericalmethodsguy]

@phatcow27 As h decreases, the accuracy increases.  By making h smaller, one can use the resulting values to quantify the accuracy of the result, and hence develop an automatic ODE solver.

[gneupane]

nice video

[gneupane]

nice video

[BearsDkills]

I NEED improved Euler's method.  Do you have any videos for that??

[sooeyz]

Thank you for the tutorial! 

[gntinos]

Thanks a lot for the time spent to create that helpful tutorial!

[mohkam03]

how do i get h is the question only states there are two steps of equal size?

[numericalmethodsguy]

@mohkam03 The user chooses h. It is chosen to be same for all steps to keep the programming simple and scientific, unless you are using adaptive methods. So if the initial value of y is give at xb=0 and you want to find y at xf=5, you need to choose h so that (xf-xb) is divisible by h. Smaller the value of h, smaller will be the error in the final result.

[mohkam03]

@numericalmethodsguy I am still confused... I gives me f(1)=-2. Dy/Dx=x-y-1. It wants me to solve for F(1.4) using Euler's method, starting at x=1 while using two steps of equal size... I used .4 for my n and I got -1.52, but the answer is -1.24...

[numericalmethodsguy]

@mohkam03 Give me the complete problem statement as given.

[mohkam03]

@numericalmethodsguy i figured it out! thank you for the help!

[Raguvian]

Thanks a lot, your explanation was much easier to understand than my professor's explanation of this method.

[bournefury]

Amazing videos sir! This just saved me on a calc test!

[gorski1986]

where does he get x(0) = 0 from?

[numericalmethodsguy]

@gorski1986 The initial value of y is given at x=0. So x subscript 0=0.

[drmehengele]

@gorski1986 yeah, and shut the fuck up. It´s obvious! hahah you dumb fuck, learn math you motherfucking cocksucking shithead! damn you be stupid!

[Monatee]

thanks!

[parthibangemini1985]

awesome teaching

[ralex321]

Thanks for reteaching me Euler's Method. This thing always gets me.

[Coutureprincess0303]

How would I find the true value?

[numericalmethodsguy]

Go to the playlist on the numericalmethodsguy channel, and see the primer on ODEs.  See the first video.

[markov2b1]

Great job. Excellent teaching. THe only thing i want to mention, you need to slow down when you say "particular". You kind of say it really fast, like purrrticular. Its pronounced kind of like POR-TICULAR. The OR sounds like Hour , ow . But its sort of in between

[numericalmethodsguy]

Thanks. Next time I will be "particular" about saying particular.

[hotbaonguyen92]

Thank you this lesson is easier then what my Ap calcus book says

[bsanghera05]

after so many tries of trying to learn this soo many ppl trying to teach me this video has finally made it clearly explained follow the steps and you got your answer thank you sooo much =D

[saab93secv]

Thank you so much! I knew that Euler's Method was simple, but it is rare to see it explained well.

[nitaiwhelan]

thats life made simple.....

keep uploading lectures their brilliant...very clear and understandable.

[AbhishekPanigrahi]

yo!!.... wonderful easy to understand presentations....

life seems a whole lot simpler with these lectures!!....if only my professor's lectures were half as interesting.....

anyways thanx a lot ...keep uploading more videos ...luking forward 2 it

[lovelandia1]

You helped me a lot , now I can understand Euler's method. BUt there is something I don't understand here. what if you are given something like this: x'-x²=1 where x(0)=1 and you are asked to to solve it numerically on interval , let's say [0,0.6] . How can I use Eulers' method to solve this numerically?

[lovelandia1]

All your examples none of them which asked to solve on specific intervals. So, I was asking myself if like where you f(yi,xi) that in this case can then be f(0,0.6)=x²+1

I just don't understand well

anyone to help please?

[supadawg1989]

thank you for this! This really helped me understand this!

[Mainichifuafua]

Thank you Dr. Kaw. This was of great help.

No one is more cherished in this world than someone who lightens the burden of another. Thank you.

[daringredevil4life]

Very helpful presentation. Kindly carry on the good work!!!

[akensim]

Dr. Kaw, thank you very much for producing these mini lectures. They are extremely useful and of immense value to all of us.

[ZwolfZki]

Nice clear presentation...

[numericalmethodsguy]

What do un mean that the method is not the same. Euler's method cannot be different from one person to another. Are you using the modified Euler's method?

[wizardroolz]

hey kaw!..ur method and mine isn't the same bt could gt the same ans...nice job!

[numericalmethodsguy]

What made you think that my name is Dr. Kumar. If this is a joke, I like it; if not, my name is Dr. Kaw.

[cokecamilo]

It was a joke lol...

but seriously speaking: this was very helpful.

[cokecamilo]

Thanks for the help Dr. Kumar!

[999madcows]

same, I have my AP Calc BC test today. Saved me!

[yellowspottedtoad]

You rock! You've just saved me from totally failing

[Bobward]

thanks a bunch!

[blkscreen15]

thanks for the help

[servos1988]

04:03:

5+(1)*2=8

WTF?! :)

[numericalmethodsguy]

It should be 5+(1)*3=8. Thanks for pointing it out. The 2 is a typo but the answer is correct as h=3. But use of WTF is not necessary to convey your sentiment. I will add an annotation to the video.

[servos1988]

No problem. English isn't my motherlanguage so I appologize for any inappropiate language.

Yea the answer is correct anyways.

[numericalmethodsguy]

The formula would not change. You would use h=-1.5 for two steps to get to y(-3.0). The only restriction is that the ODE needs to be valid for x>=-3.

[CHARLIEGTG]

how would you do instead of y(3).. you want y(-3)???? how would the formula be???