Recent content by stvoffutt

I was looking at a research paper the other day. In the paper they described some of the results from an experiment. They looked at two of the variables recorded in the experiment, mass and velocity. They looked at mass independently. First, they took the median of the mass. They then had two...

I calculated the num_steps the way I did because I usually need to change the step_size for one problem. For example I would solve a problem with step size k = 1/4,1/8,1/16,... etc. I ran the program and Matlab does not give INF in any spaces within the solution vectors but the v vector is...

Thank you everyone for your replies. I suppose our instructor just gave this exercise to us to illustrate the instability of forward/backward Euler method for this particular problem. I tested my program on another system which gave me the correct answer so I know it's not my code. What...

Homework Statement Solve the following system for 0<t<5 u^\prime = u-e^{-2t} v, u(0) = 1 v^\prime = u+3v, v(0) = -2 using Forward Euler method and implement the numerical scheme into a MATLAB code. Homework Equations Forward Euler : \vec x^(\prime)_{n+1} = \vec F(t,\vec x)...

I figured it out. Thanks.

Homework Statement I need to evaluate a function using 4-point GQ. Homework Equations GQ theory The Attempt at a Solution I have got more of a programming issue in MATLAB. I am new to MATLAB. Actually this is for a numerical analysis course where we kind of learn MATLAB on the...

y_j=y_{j-1}-hy^{\prime}_{j-1}+\frac{h^2}{2!}y^{\prime \prime}_{j-1}+O(h^3)? I'm sorry. I am having a hard time trying to keep all of this straight. This is my first course in numerical analysis.

y_j=y_{j+1}+hy^{\prime}_{j+1}+\frac{h^2}{2!}y^{\prime \prime}_{j+1}+O(h^3)?

I'm not sure how to expand y_j in terms of y_j+1. Can you point me in the right direction?

So should I expand like this? y_{j+2}=y_{j+1}+2hy^{\prime}_{j+1}+\frac{4h^2}{2!}y^{\prime \prime}_{j+1}+\cdots and do the same thing for y_{j-2}?

Homework Statement By using Taylor expansion, derive the following two-step backward differentiation which has second order accuracy: \frac{3y_{j+1}-4y_j+y_{j-1}}{2h}=f(t_{j+1},y_{j+1}) Homework Equations Taylor expansion ODE y^{\prime}=f(t,y) , y(0)=\alpha The Attempt...

Wow, never mind. I feel dumb. What I pulled out of the sum is not \psi(x). You need to multiply that product by (x-x_k) for it to be \psi(x). Fun with definite products - not my strong suit.

Homework Statement Consider the Lagrange Polynomial approximation p(x) =\sum_{k=0}^n f(x_k)L_k(x) where L_k(x)=\prod_{i=0,i\neq k}^n \frac{x-x_i}{x_k-x_i} Let \psi(x)=\prod_{i=0}^n x-x_i. Show that p(x)=\psi(x) \sum_{k=0}^n\frac{f(x_k)}{(x-x_k)\psi^\prime(x)} Homework Equations None...

Homework Statement A 2 \mug sample of {}^{47}Ca is encased in a lead sphere. What is the photon intensity 5 cm from the source? Use some of the tables in your book to find the required information. Homework Equations Flux/Intensity of photons from a point source...

Homework Statement Using the definition of |x-a|<delta implies |f(x) - L|<epsilon, prove that lim x->0 x^n*sin(1/x) holds for all n belonging to natural numbers. Homework Equations Definition of a limitThe Attempt at a Solution Ok, so when I see "prove for all n belonging to natural numbers" I...