Recent content by Gengar

Well making the substitution x=e^t does indeed get the solution, you should get via chain rule: \frac{d}{dx}=e^{-t}\frac{d}{dt}, \frac{d^2}{dx^2}=e^{-2t}(\frac{d^2}{dt^2}-\frac{d}{dt}) which when substituted into your original equation should yield an inhomogeneous 2nd order ODE with constant...

Yeh... After solving numerically I realized that I just hadn't thought about the fact that the waves must propagate at speed 1 and u=0 for all x>t. So a quick bit of algebra gives: u(x,t)=H(t-x)sin(w(t-x)) simples

Hi, so the problem is this: I am trying to solve (analytically) the wave equation with c=1: u_{xx}=u_{tt} on x,t>0 given the initial conditions u(x,0)=u_{t}(x,0)=0, u(0,t)=sin(wt) I know how to solve on semi-infinite domains for quite a few cases using Green's Functions, Fourier Transforms...

Hiya. I have to solve this bad boy under the assumptions that f, f' and f'' tend to 0 as |x| tends to infinity: 1/2(f')^2 = f^3 + (c/2)f^2 + af + b where a,b,c are constants. My thoughts are use Fourier Transforms to use the assumptions given, but not sure how to do them on these terms...

Agreed, but I'm only interested in macheps for my computer. Would it be wrong to factorise a + εa = (1+ε)a? In which case the problem is unchanged - and for this task I don't need to take multiplication/division into account. If my factorisation is incorrect, then what would be the smallest...

You're getting slightly confused, but did arrive at the answer kinda. Basically for x large, the x^3 terms on both the denominator and numerator will dominate each expression. Since they are both of degree 3 (that is the highest power of x is 3 for each) we simply look at the coeffecients of...

Or simply consider derivatives: d/dx (e^x) = e^x and d/dx(x^e)=ex^(e-1) These tell you how fast each function is increasing at each x, hence you can work out which function is increasing faster at each x.

Well firstly write v'= -(xy+v)/x = f2(x,y,v) instead of what you wrote. Your usual k1,k2,k3,k4 for first order RK now became vectors of dimension 2 ie (k1, j1), (k2,j2)... Then just apply the standard RK method for working them out, being careful as you will need the j's to work out the k's and...

Simple enough - I'm just trying to find the smallest positive real number, ε, such that 1 + ε ≠ 1 in MATLAB (double precision). So the value 'eps' in MATLAB is actually not quite defined this way, and using this program min = 0; max = 1; test = 1; while test~=(min+max)/2 test =...

Ah thanks, yeh that's been bugging me (geddit?) for ages. Cheers

I'm a newbie to all things programming, and have to write a program implementing the Euler method to approximate an ODE. Anyways, the program works but when I use the function I wrote I get an extra matrix of zeroes above the desired output, which I don't understand as I have suppressed the...

You need to consider 3 cases: 1. x is in O 2. x is a boundary point of O 3. x is neither in O nor a boundary point of O Should be straightforward from there

Correct. Hope your anxiety is eased