Explain the two terms in equation 
that comprise the flux,
Js. Solve the ODE and show how the general solution is
given by 
where 
Cm 4(1 - W) + a2 exp( Pe
Homework Answers
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Explain the two terms in equation that comprise the flux, Js. Solve the ODE and show how the gen...
Please help solve this, using the equation to get through the problem. Additional information: where the...
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...
ASAP PLEASE e) Explain the idea of the Gauss integration formula. f Show on a figure the local and global truncation error for the first two iterations of a ODE solver g) Solve graphically the ODE h)...
ASAP PLEASE
e) Explain the idea of the Gauss integration formula. f Show on a figure the local and global truncation error for the first two iterations of a ODE solver g) Solve graphically the ODE h) Explain how numerical adaptive ODE solvers works i) When is a numerical method for solving differential equations considered to be dy dx unstable ? Which parameter(s) is (are) influencing this stability (or instability)? j In general the total error done by any numerical...
Consider the IVP, 1. Apply the Fundamental Existence and Uniqueness Theorem to show that a solution...
Consider the IVP, 1. Apply the Fundamental Existence and Uniqueness Theorem to show that a solution exists. 2. Use the Runge-Kutta method with various step-sizes to estimate the maximum t-value, , for which the solution is defined on the interval . Include a few representative graphs with your submission, and the lists of points. 3. Find the exact solution to the IVP and solve for analytically. How close was your approximation from the previous question? 4. The Runge-Kutta method continues...
2. A simple pendulum with length satisfies the equation a) If 0 is the amplitude of...
2. A simple pendulum with length satisfies the equation
a) If 0 is the amplitude of the oscillation, show that its
period T is given by
where
and
.
We were unable to transcribe this image9 S2n π/2 do T= asin 6 woJo V We were unable to transcribe this image0 Syク 2. A simple pendulum with length ( satisfies the equation (a) If θ0 is the amplitude of the oscillation, show that its period T is given by 1...
help me please , By using MATLAB How can I plot the solution of linear diffrential...
help me please , By using MATLAB
How can I plot the solution of linear diffrential system ? I
want the code in general case
We were unable to transcribe this imageclose all clear MATLAB Code: clc A= [1 0 1; 0 0 0;00-1]; % Coefficient Matrix Xo = [5 76]'; % Initial condition V, D = eig(A); % Get the Eigen values and Eigen vectors % General Solution: X=Sum of {c_i*exp(L_i*t) *V_i % where c_i are constants, L_i are...
all parts, please For this problem, we'll solve the 3D wave equation in a box. The...
all parts, please
For this problem, we'll solve the 3D wave equation in a box. The Laplacian in 3 dimensions is a2 vu= a2 a2 ou + ay? U= and the wave equation is 22 a2 at24 = 1 (a) (3 Points) Use separation of variables with ur,y,z,t) = S(x, y, z)T(t) to get a spatial PDE and a temporal ODE for this problem, call the separation constant A. Show all your work! (b) (3 Points) The spatial equation should...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
Problem 2. (15 points) Solve the following Laplace's equation in a cube as outlined below. au...
Problem 2. (15 points) Solve the following Laplace's equation in a cube as outlined below. au au au 2,2 + a2 + a2 = 0, on 0<x<1, 0<y<1, 0<?<1, (0, y, z) = (1, y, z) = 0, (x, 0, 2) = u(x, 1, ) = 0, (x, y,0) = 0, u(x,y, 1) = x. (a) Seek a solution of the form u(x, y, z) = F(x) G(v) H(-). Show that with the appropriate choice of separation constants, you can...
i am very confused with these questions. can someone help me solve? and can you explain...
i am very confused with these questions. can someone help me
solve? and can you explain neatly and clearly? will rate, thank
you.
1. In this experiment, you will be generating time measurements that have both random uncertainty (Stran) and systematic uncertainty (dtsys). Using Eq. 4 as a starting point, write down an equation that will allow you to calculate &t from Stran and otsys 2. The acceleration due to gravity is related to the time, t, it takes the...
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...
ASAP PLEASE
e) Explain the idea of the Gauss integration formula. f Show on a figure the local and global truncation error for the first two iterations of a ODE solver g) Solve graphically the ODE h) Explain how numerical adaptive ODE solvers works i) When is a numerical method for solving differential equations considered to be dy dx unstable ? Which parameter(s) is (are) influencing this stability (or instability)? j In general the total error done by any numerical...
2. A simple pendulum with length satisfies the equation
a) If 0 is the amplitude of the oscillation, show that its
period T is given by
where
and
.
We were unable to transcribe this image9 S2n π/2 do T= asin 6 woJo V We were unable to transcribe this image0 Syク 2. A simple pendulum with length ( satisfies the equation (a) If θ0 is the amplitude of the oscillation, show that its period T is given by 1...
help me please , By using MATLAB
How can I plot the solution of linear diffrential system ? I
want the code in general case
We were unable to transcribe this imageclose all clear MATLAB Code: clc A= [1 0 1; 0 0 0;00-1]; % Coefficient Matrix Xo = [5 76]'; % Initial condition V, D = eig(A); % Get the Eigen values and Eigen vectors % General Solution: X=Sum of {c_i*exp(L_i*t) *V_i % where c_i are constants, L_i are...
all parts, please
For this problem, we'll solve the 3D wave equation in a box. The Laplacian in 3 dimensions is a2 vu= a2 a2 ou + ay? U= and the wave equation is 22 a2 at24 = 1 (a) (3 Points) Use separation of variables with ur,y,z,t) = S(x, y, z)T(t) to get a spatial PDE and a temporal ODE for this problem, call the separation constant A. Show all your work! (b) (3 Points) The spatial equation should...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
Problem 2. (15 points) Solve the following Laplace's equation in a cube as outlined below. au au au 2,2 + a2 + a2 = 0, on 0<x<1, 0<y<1, 0<?<1, (0, y, z) = (1, y, z) = 0, (x, 0, 2) = u(x, 1, ) = 0, (x, y,0) = 0, u(x,y, 1) = x. (a) Seek a solution of the form u(x, y, z) = F(x) G(v) H(-). Show that with the appropriate choice of separation constants, you can...
i am very confused with these questions. can someone help me
solve? and can you explain neatly and clearly? will rate, thank
you.
1. In this experiment, you will be generating time measurements that have both random uncertainty (Stran) and systematic uncertainty (dtsys). Using Eq. 4 as a starting point, write down an equation that will allow you to calculate &t from Stran and otsys 2. The acceleration due to gravity is related to the time, t, it takes the...
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