Euler's method Definition and 74 Threads

Homework Statement Well, I'm having problems with this script, I'm taking my first course on differential equations, and I am trying to write a script that approximates the values of the solution of a differential equation, and compares them to the exact solution using a table of values, it...

Hi all. I've been having a bit of trouble just understanding Euler's method, which I need to know (and probably should have known for a while now) for a question on an assignment. I'm going to provide an example with confusing wording (at least to me) and show what I've done to try to...

Homework Statement y' = y - x - 1, y(0) = 1, h = .25 Homework Equations The Attempt at a Solution y1 = 1+(.25)*(1-0-1) = 1 y2 = 1+(.25)*(1-1-1) = .75 This is not what the book has, but it is organized weird to me. It asks for EM twice, first w/ step size h=.25, then h=0.1...

Please help me with this problem! I have no clue. I know how to deal with only dy/dx. But this includes dy/dx and dz/dx...:cry: Please see the attachment :) Step size h = 0.2 range x = 0 to 1 y(0) = 2 z(0) = 4 Thank you, Maya

Homework Statement Hi guys, I have the following problem and I don't know how to start. I am given that W = 0.5, X(0) = 0, Iab = 20m and ha = 5m \frac{dy}{dx}=0 and \frac{dy^2}{d^2x}=\frac{W}{T}\sqrt{1 + (\frac{dy}{dx})^2} I am told to convert the 2nd order ODE to two 1st...

Hi I'm doing a practice paper for a past mathematical modelling exam. I've attached the problem What I'm having trouble with is simplifying the equations and variables into a differential equation that is solvable with Euler's Method. What I have currently is the sqrt(h1-h2) in the...

I wondered if someone could do this for me so that i can use it as an example to learn from, it is from a past paper for an exam i will be sitting soon. Suppose that a sky diver steps out of an aeroplane at an altitude of 10,000ft and that his downward acceleration is given by: dv/dt = 32...

y_{2,n} + 0.1(2y_{2,n} - y_{1,n} + 4t) If y_{1,0}=1 and y_{2,0}=1, what is y_{2, 0.1}? 1.1 or 1.14?

Hi all. Could someone give me a hand with this: Using Euler's method find an approximate solution to the IVP using step size h = 0.1 \frac{dy}{dx} = 4xy + 3 , y(0)=0 I know how to use Euler's method for something simple like \frac{dy}{dx} = x + y But I'm just not to sure what...

Suppose an object of 20kg is shot upward with an initial velocity of 20m/s. The drag coefficient I've chosen is 0.25, and gravity is 9.8m/s. I'm trying to calculate the terminal velocity using Euler's Method (using a C prog), and then graph the data using openoffice. I know I am converging to...

I'm trying to make a program that can approximate a differential equation via the Euler's method. Here is my program : Program diff implicit none Real :: t_0, x_0, t_f, k_j, h Real :: t,x Integer :: n,j Write(*,*)'Chose t_0 and x_0' Read(*,*)t_0, x_0 Write(*,*)'Chose t_f'...

When solving the initial value problem y ' = 2y-x, y(11)=6 using Eulers method with h=0.2, y0=? I know how to solve Euler's equations with the formula yn = yn-1 + F(xn-1 + yn-1)(h), however I'm not quite sure how or what they want in this particular case. Can anybody please help me out if...

Homework Statement Four dogs start running from the corners of a field 100m square. Label the dogs A, B, C, D clockwise in that order. Dog A chases dog B which chases dog C which chases dog D which chases dog A. Here 'chase' means that the direction in which the chasing dog moves is directly...

Homework Statement http://img299.imageshack.us/img299/9060/untitled1oi9.jpg The Attempt at a Solution Is this the correct method to attempt this question? http://img179.imageshack.us/img179/5024/untitled2dr4.jpg My final value for 2 is -21.65816774, and I have no idea if that...

We just started learning how to find diffrencial equations using the eulers method. I heard there is a programm in a calculator that let's you do that. I have a ti 84 I don't know the name of the program if you can be kind and give me the website it would be appreciated. My calculus book had...

Hello, For Euler's Method of Numerical Approximations, my book (Boyce&DiPrima) gives this algorithm: Step 1: define f(t,y) Step 2: input initial values t0 and y0 Step 3: input step size h and number of steps n Step 4: output t0 and y0 Step 5: for j from 1 to n do Step 6: k1 = f(t,y)...

I'm having trouble solving first order differential equations for euler's method. right now I'm trying to figure out: y' = x + y y(0) = 1 i have: dy/dx - y = x p(x)=-1 , q(x)=x u=e^(-x) y=e^x [integral](xe^-x)dx .. i don't think I'm doing this right, where am i going...

I need some clarification please the question is: -Using Euler's method with h = .25 given dy/dx = ycosx ,y(0) = 1 on the interval 0 <= x =< pi/4. are the X's : pi/12, pi/6, pi/4 OR .25, .50, .75 ?? some help please que.

this is the classic euler's method, but i'd like to modify it so that it can handle two-dimensional systems on the form x'=... y'=... what needs to be done? function [X,Y] = euler1(x,y,x1,n) h=(x1-x)/n; X=x; Y=y; for i=1:n y=y+h*f(x,y); x=x+h; X=[X;x]; Y=[Y;y]; end X Y...

I somewhere read that Euler proved that primes are infinite by proving that the series 1/2 +1/3 + 1/5 +... diverges. Can anybody tell the proof? Aditya

I understand how the (local) error for euler's method of integration is derived from the perspective of the taylor expansion and inequality. However, I don't really see why taylor's equation needs to be invoked, since the euler method can also be derived as a tangent line approximation. How then...

Consider the initial value problem y^{\prime} = \frac{3t^2}{3y^2 - 4} \mbox{,} \qquad y(1) = 0\mbox{.} (a) Use Euler's method with h=0.1 to obtain approximate values of the solution at t=1.2\mbox{, }1.4\mbox{, }1.6\mbox{, and } 1.8. (b) Repeat part (a) with h=0.05. (c) Compare the...

Hi As the title says i am trying to find a good example (easy diffrential equation) to demonstrate Euler's method to explain it easily without a lot of calculations, help is appriciated

Hello, I am having trouble understanding a question in relation to Euler's method. Basically, the question goes something like Euler's method is solved to solve the differential equation \frac{{dy}}{{dx}} = \log _e \left( {4 - x^2 } \right), with a step size of 0.05 and initial condition y =...