In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who treated it in his book Institutionum calculi integralis (published 1768–1870).The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method.
Homework Statement
Use either image charge method of separation of variables to solve:
The distance between two large, grounded parallel conducting plates is 4x. Between them, two point charges +Q and -Q are inserted and have a distance x and 3x from one of the plates. (A line connecting the...
Homework Statement
Determine the exit speed(initial velocity) of a marble exiting a launcher shot from a table.
The height of the table, distance of the x component and the time can be measured. t=? Vi=? Vix=?
Homework Equations
d= vi * t + 0.5*g*t^2
Vi^2=Vix^2*Viy*2
The Attempt at a Solution
I...
What is "Negative Gradient" ? and what is "Gradient Descent Method" ? What is the difference and relationship between them ?
What is the benefit each of them ?
Homework Statement
Two point charges of equal value are placed a distance 2b from one another. In the middle, there is a grounded conducting sphere. What is the minimum radius of the sphere required to cancel out the repelling force between the two charges? (Solve using Image Charge Method)...
Hi all
What if instead of charges and a surface, we were given a set of charges and image charges and have to find the surface, how would you do that?
This is actually part of my homework but I'm pretty sure he doesn't want us to prove it mathematically (the case is obviously a sphere) so I...
Here is the question:
We are not given the wavefunction so in this instance would I use the variational method? i.e. should I guess the wavefunction and apply:
E_{guess} = \frac{< \Psi_{guess} \mid H \mid \Psi_{guess} > }{< \Psi_{guess} \mid \Psi_{guess} >}
I am really unsure about how to...
Homework Statement
From the above circuit find VCB and VDG
Know Data:
VE = 0 (ground)
Homework Equations
KCL and Ohm's Law are used in Node Voltage Method.
The Attempt at a Solution
I decided I would determine the node voltages then work out VCB and VDG afterwards.
1. KCL and Ohm's law at...
Homework Statement
Use Euler's method with h=0.05 to find approximate values for the solution of the initial-value problem y'=2x^2+3y^2-2, y(2)=1 at x=0.1, 0.2, 0.3.
Homework Equations
None.
The Attempt at a Solution
Here's my work:
y'=2x^2+3y^2-2, y(2)=1
f(x, y)=2x^2+3y^2-2, x0=2, y0=1...
medicalxpress.com/news/2014-11-scientists-mechanism-spontaneous-hiv.html
Sorry, if it's in the wrong forum, is this method feasible?. I know in the genetic code, there are many stretches that resemble virus code(apparently silenced) , it's quite interesting they are using that as a starting...
Homework Statement
The problem is a cantilive beam of length L with a triangular uniform load or W. The solution is to find the slope and deflection at the end by moment area method. My solution is not matching the textbook solution of wl^3/8EI and 11wL^4/120EI
Homework Equations
First...
Homework Statement
Find the general solution by finding the homogeneous solution and a particular solution.
y'' + 4y' = x
Homework EquationsThe Attempt at a Solution
First, I found the corresponding solution to the homogeneous differential equation:
y'' + 4y' = 0
r^{2} + 4r = 0
r_1 = 0...
I am creating a traffic flow model, modelling the flow of traffic as fluid with density and velocity. I am using the method of characteristics to solve the model but I have run into a problem.
The model I have is:
$\frac{\partial\rho}{\partial t}+c(\rho)\frac{\partial\rho}{\partial x}=0$...
hi guys,
my professor told me in the class that when we would like to determine green function there are two general method i.e using image charge and using orthonormal eigen function. However I don't understand what are the specific differences between them. Anybody can help me? Moreover in the...
Can someone please help me understand how two-antenna method is used to measure gain of an antenna ?
I could't even find literature on it, please if anyone could even suggest any document that would also be great.
Thanks.
Homework Statement
measure the velocity of sound in the air using tuning fork and a pipe closed at one end
method a: End Correction involves applying a correction factor to the first resonant length based on the diameter of the tube used.
method b: Second Resonant Length involves finding two...
Homework Statement
So this is more of a general question as I'm trying to follow the book's way of solving the problems and it's not working.
This is what the book says:
Always assume the unknown member forces acting on the joint’s
free-body diagram to be in tension ; i.e., the forces “pull”...
when i use this MATLAB code but with rectangular pulse shape instead of chirped pulse i didn't get the predicted output , so is there a limitation with this method in case of rectangular pulse or the MATLAB code is wrong...
Homework Statement
Use the reduction of order metho to find a second linearly independent solution. What is the general solution of the differential equation?
y'' - y = 0
y_1(x) = e^x
Homework Equations
Reduction of order formula
The Attempt at a Solution
First, I set:
y = ve^x
y' =...
Given a warren truss, where the load is 2kN/m so the weight per joint is 10kN, since the ends are supported by ground not truss, can anyone please verify my way of solving for the tension and compression at point B.
See attachment
Your help is greatly appreciated.
So I figured out that AB is...
Homework Statement
y'' + 4y' + 4y = 0 ---- y(0) = 1, y'(0) = 5
Find the exact solution of the differential equation.
Use the exact solution and Euler's Method to compute Euler's Approximation for time t = 0 to t = 5 using a step h=0.05. Plot Euler's & Exact vs. t and plot Error vs. t. Then...
Hello,
I am in an introductory undergraduate course on ODEs, currently on the method of variation of constants to solve nonhomogenous equations.
I am noticing that with many of these problems, when solving for constants after plugging in my guessed values for y I end up with enormous...
Hello,
I was going through Perron method within the text and came across Lemma 1 which states that if u1,u2 are subharmonic on some domain D and satisfies Cauchy boundary conditions (for example), then so does max(u1,u2). I am quite confused in terms of proving the statement. How would one...
Hello! I need help to integrate the square root of:
p x2 + x4
by the method of substitution, p is just a constant. I've been trying for a long time but I can't get it right. I know the answer and it still doesn't help. Thanks! (sorry, I don't know the Latex stuff)
If we want to know whether a certain range of numbers, say between x and y, contain prime or not.
Do we use only the division method by all the prime less than the square root of y. If all the number are divisible, then there are no prime in that region.
Because according to the above method...
Okay, so here's a question I'm working on:
Question: Present the transition diagram or table for a DFA that accepts the regular set denoted by the expression (0+1)* (010 + 11) (0 + 1)*
Here is my DFA:
https://dl.dropboxusercontent.com/u/5778771/Midterm1SampleQuestion1.jpg
But it took me a...
Hello. This is not homework, so I am posting this here because I feel this is the right place to do so.
How do I find charges Q1, Q2 and Q3? The answers are given as follow:
Q1 = Q3 (This is due to the symmetrical arrangement)
= 6.97 x 10^-11 [C]
Q2 = 1.44 x 10^-11 [C]
I really...
Hi there. The example to obtain the electric potential in the region z>0 by the method of images for a infinite grounded conducting plane, with a point charge q located at a distance d is a typical example of the application of the method of images.
If we consider that the plane is located in...
How do we detect if there is more than 1 exoplanet orbiting a star using radial velocity method?
I read this but I didnt understand it. Can someone explain the answer in Laymans terms?
"Multiple planets will cause a stars radial velocity curve to show two periods: a long gradual change due...
Homework Statement
The first order linear equation of the form:
\frac{dy}{dx} + ay = b
where a and b are constants, can be solved both by the integrating factor method and by separation of variables. Solve the equation using both methods to see that you get the same solution...
Homework Statement
I need to find the roots of a given equation using the secant method and matlab. I have already found all the roots, but I am also asked to find the rate of convergence for the method empirically, meaning that they want me to find the order of convergence through the set...
Homework Statement
Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y=2x+15 and the parabola y=x2 about the following lines:
a) The line x=5 b) The line x= -3 c) The x-axis d) The line y=25
Note: leave answer in terms...
Homework Statement
Find the general solution to the indicated equation:
cos(x)y' + ysin(x) = 1
Homework Equations
e^\int p(x)\,dx * y(x) = int\ f(x)\, dx e^\intp(x)\,dx + C
The Attempt at a Solution
Ok, I am having trouble getting started with this problem because I am not...
Homework Statement
Use the mesh-current method to find v0.
Find the power delivered by the dependent source.
Homework Equations
v1+v2+..vn=0
i=v/R
p=iv
The Attempt at a Solution
eq #1)-i1*10+i2*20=25V
eq #2) i2*20+i2*24+6iΔ=0
eq #3) iΔ*14=21
eq#3) iΔ=1.5A
eq#3 sub into eq#2)...
Homework Statement
Use the node-voltage method to find v0 in the circuit below.
Homework Equations
i1+i2+...in=0
i=v/R
The Attempt at a Solution
So I set my reference node to the top of the middle line(above 25Ω)
Equation...
24V/(20+80)Ω+v0/25+.004A=0
Now I can solve for...
I'm supposed to be doing a project. Here is what it says to do.
I tried to copy and paste the directions in here but some of the equations are not turning out on this page as expected, so I have uploaded the project.
Can anyone tell me how I need to start or what to do please? The...
I was reading the finite element method in engineering by Rao and in the first example he ends up with a matrix that is singular.
The matrix is the following:
\begin{pmatrix}
2 &-2 & 0\\
-2 & 3&-1\\
0&-1& 1
\end{pmatrix}
Which is a symmetric matrix as far as I can remember...
Hi,
I'm having trouble with this one.
Homework Statement
Find a particular solution of the second-order homogeneous lineal differential equation
x^2y'' + xy' - y = 0
taking in account that x = 0 is a regular singular point and performing a power series expansion.
Homework...
Hi guys , i am solving this equation by Finite difference method.
(dt2/dx2 + dt2/dy2 )= -Q(x,y)
i have developed a program on this to calculate the maximum temperature, when i change the mesh size the maximum temperature is also changing,
Should the maximum temperature change with mesh...
Homework Statement
Plot the transient conduction of a material with k = 210 w/m K, Cp = 350 J/kg K, ρ = 6530 kg/m3
Where the material is a cylinder, with constant cross sectional area and is well insulated. The boundary conditions for the cylinder:
T(0,t) = 330K
T(l,t) = 299K...
I've posted a method below.
I'm experimenting with local variable declarations in java. Actually, a compiler error in eclipse has made me reconsider what I understand about local variables. Why can't the local variable, String final, be created inside my if statement? Why, instead, would...
Homework Statement
Consider the following pair of coupled first order ODEs
\dot{y_{1}} = y_{2} with ##y_{1}(0) = 1##
\dot{y_{2}} = -y_{1} with ##y_{2}(0) = 1##
Use the Euler integration method with a step-size ##h = 1## and fill out the entries in the table below
\begin{bmatrix}...
Homework Statement
Complete the following MATLAB function that computes the integral ##\int_{-2}^{5} f(x)dx## of the function
##f(x)## plotted in the figure below, after N trials using a Monte Carlo method. Take all the required
numerical inputs from the figure shown below.
Hint: Generate a...
Simplex method - infeasible
I'm looking at some linear optimization problems. In one example I must be missing something, maybe someone can point it out. Here's the example:
\begin{align*}
\textrm{max } f(\textbf{x}) = & 2x_1 + x_2 \\
\textrm{subject to} & x_1 + x_2 \leq 5 \\
& -x_1...
Homework Statement
Show that if given \mathbf{x}_0, and a matrix R with spectral radius \rho(R)\geq 1, there exist iterations of the form,
\mathbf{x}_{n+1}=R\mathbf{x}_0+\mathbf{c}
which do not converge.
The Attempt at a Solution
Let \mathbf{x}_0 be given, and let...
I don't really understand what is the need of giving feedback in the magnetostriction method to produce ultrasonic waves.
I am thinking of just winding a single rod over a nickel rod and then connecting then connecting the 2 ends to a battery. When the current is passed,magnetic field...
Region bounded by x^2-y^2=16, y=0, x=8, about y-axis
Integrating with respect to y, my lower and upper bounds are $-4\sqrt{3}$ and $+4\sqrt{3}$, respectively.
V=\pi \int_{-4\sqrt{3}}^{4\sqrt{3}} 64-(16+y^2)\,dy
=2\pi \int_{0}^{4\sqrt{3}} 48-y^2\,dy
=2\pi (192\sqrt{3})
=256\pi
My textbook...