Homework Answers
Add Answer to:
2. The explicit Euler and 4th order Runge-Kutta schemes for solving the following ordinary differential equation do f(6...
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn...
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following ordinary differential equation and initial conditions as a sys- tem of first order equations: y(1)=1, /(1) 3. (b) Use the second order explicit Runge-Kutta scheme with one step to compute an approximation to y(1.2).
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following...
Solve the ordinary differential equation below over the interval 0 sts 2s using two different methods: the Euler method and the second-order Runge-Kutta method (midpoint version). Begin by writin...
Solve the ordinary differential equation below over the interval 0 sts 2s using two different methods: the Euler method and the second-order Runge-Kutta method (midpoint version). Begin by writing the state space representation of the equation. Use a time step of 1 s, and place a box around the values of x and x at t- 2 s obtained using each method. Show your work. 20d's +5dr +20x = 0 dt d x(0) = 1, x'(0) = 1
Solve the...
3. (a) Express the following ordinary differential equation and initial conditions as an autonomous system of...
3. (a) Express the following ordinary differential equation and initial conditions as an autonomous system of first order equations: 2"-223z = 2, '(0)= 1 z(0) 0, (b) Consider the following second order explicit Runge-Kutta scheme written in au- tonomous vector form (y' = f(y)): hf (ynk kihf (yn), k2 yn+1 ynk2. IT Use the second order explicit Runge-Kutta scheme with steplength h compute approximations to z(0.1) and z'(0.1) 0.1 to _
3. (a) Express the following ordinary differential equation and...
Numerical Methods for Conservation Laws, Randall J. LeVeque, Ed. 2. question/ do 2nd order explicit Runge-Kutta...
Numerical Methods for Conservation Laws, Randall J.
LeVeque, Ed. 2.
question/ do 2nd order explicit Runge-Kutta
hint
1. Consider the linear equations, Use central difference for the spatial discretization. Derive the stability condition for the schemes with the followinor temporal discretization α2 Ζα where α v sin θ α2 |λ| > 1 for any positive k when θ π/2 .
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3,...
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
use matlab Assignment: 1) Write a function program that implements the 4th Order Runge Kutta Method....
use
matlab
Assignment: 1) Write a function program that implements the 4th Order Runge Kutta Method. The program must plot each of the k values for each iteration (one plot per k value), and the approximated solution (approximated solution curve). Use the subplot command. There should be a total of five plots. If a function program found on the internet was used, then please cite the source. Show the original program and then show the program after any modifications. Submission...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equation...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equations is 1hg(n,un,vn), un+1 Consider the following second order differential equation d2 0cy-6, with v(1)-1 and y'()-o Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal...
Ordinary Differential Equations (a) Write a Python function implementing the 4'th order Runge-Kutta method. (b) Solve...
Ordinary Differential Equations (a) Write a Python function implementing the 4'th order Runge-Kutta method. (b) Solve the following amusing variation on a pendulum problem using your routine. A pendulum is suspended from a sliding collar as shown in the diagram below. The system is at rest when an oscillating motion y(t) = Y sin (omega t) is imposed on the collar, starting at t = 0. The differential equation that describes the pendulum motion is given by: d^2 theta/dt^2 =...
Consider the following Ordinary Differential Equation (ODE): dy = 0.3 * x2 + 0.04 * 26...
Consider the following Ordinary Differential Equation (ODE): dy = 0.3 * x2 + 0.04 * 26 – 4* y? dx with initial condition at point 20 = 0.6875: yo = 0.0325 Apply Runge-Kutta method of the second order with h = 0.125 and the set of parameters given below to approximate the solution of the ODE at the three points given in the table below. Fill in the blank spaces. Round up your answers to 4 decimals. Yi 0.0325 0.6875...
Using the Runge-Kutta fourth-order method, obtain a solution to dx/dt=f(t,x,y)=xy^3+t^2; dy/dt=g(t,x,y)=ty+x^3 for t= 0 to t= 1 second. The initial conditions are given as x(0)=0, y(0) =1. Use a time...
Using the Runge-Kutta fourth-order method, obtain a solution to dx/dt=f(t,x,y)=xy^3+t^2; dy/dt=g(t,x,y)=ty+x^3 for t= 0 to t= 1 second. The initial conditions are given as x(0)=0, y(0) =1. Use a time increment of 0.2 seconds. Do hand calculations for t = 0.2 sec only.
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following ordinary differential equation and initial conditions as a sys- tem of first order equations: y(1)=1, /(1) 3. (b) Use the second order explicit Runge-Kutta scheme with one step to compute an approximation to y(1.2).
5. Consider the following second order explicit Runge-Kutta scheme: k=hf(an, Yn) k2 = hf(2, +h, yn +ki) Yn+k2. Yn+1 (a) Express the following...
Solve the ordinary differential equation below over the interval 0 sts 2s using two different methods: the Euler method and the second-order Runge-Kutta method (midpoint version). Begin by writing the state space representation of the equation. Use a time step of 1 s, and place a box around the values of x and x at t- 2 s obtained using each method. Show your work. 20d's +5dr +20x = 0 dt d x(0) = 1, x'(0) = 1
Solve the...
3. (a) Express the following ordinary differential equation and initial conditions as an autonomous system of first order equations: 2"-223z = 2, '(0)= 1 z(0) 0, (b) Consider the following second order explicit Runge-Kutta scheme written in au- tonomous vector form (y' = f(y)): hf (ynk kihf (yn), k2 yn+1 ynk2. IT Use the second order explicit Runge-Kutta scheme with steplength h compute approximations to z(0.1) and z'(0.1) 0.1 to _
3. (a) Express the following ordinary differential equation and...
Numerical Methods for Conservation Laws, Randall J.
LeVeque, Ed. 2.
question/ do 2nd order explicit Runge-Kutta
hint
1. Consider the linear equations, Use central difference for the spatial discretization. Derive the stability condition for the schemes with the followinor temporal discretization α2 Ζα where α v sin θ α2 |λ| > 1 for any positive k when θ π/2 .
3. Consider the following stiff system of autonomous ordinary differential equations du f(u, u) =-3u +3, u(0)2 = ' dt de g(u, v) -2000u - 1000, v(0)-3 Note that 1 u<2 and -4 <v < 3 for all t. (a) Find the Jacobian matrix for the system of equa tions (b) Find the eigenvalues of the Jacobian matrix. (c) In the figure the shaded region shows the region of absolute stability, in the complex h plane, for third order explicit...
use
matlab
Assignment: 1) Write a function program that implements the 4th Order Runge Kutta Method. The program must plot each of the k values for each iteration (one plot per k value), and the approximated solution (approximated solution curve). Use the subplot command. There should be a total of five plots. If a function program found on the internet was used, then please cite the source. Show the original program and then show the program after any modifications. Submission...
Question 12 (3 marks) Special Attempt 2 A system of two first order differential equations can be written as 0 dr A second order explicit Runge-Kutta scheme for the system of two first order equations is 1hg(n,un,vn), un+1 Consider the following second order differential equation d2 0cy-6, with v(1)-1 and y'()-o Use the Runge-kutta scheme to find an approximate solution of the second order differential equation, at x = 1.2, if the step size h Maintain at least eight decimal...
Ordinary Differential Equations (a) Write a Python function implementing the 4'th order Runge-Kutta method. (b) Solve the following amusing variation on a pendulum problem using your routine. A pendulum is suspended from a sliding collar as shown in the diagram below. The system is at rest when an oscillating motion y(t) = Y sin (omega t) is imposed on the collar, starting at t = 0. The differential equation that describes the pendulum motion is given by: d^2 theta/dt^2 =...
Consider the following Ordinary Differential Equation (ODE): dy = 0.3 * x2 + 0.04 * 26 – 4* y? dx with initial condition at point 20 = 0.6875: yo = 0.0325 Apply Runge-Kutta method of the second order with h = 0.125 and the set of parameters given below to approximate the solution of the ODE at the three points given in the table below. Fill in the blank spaces. Round up your answers to 4 decimals. Yi 0.0325 0.6875...
Most questions answered within 3 hours.
-
The energy required to remove an electron from a surface of a
solid element is called...
asked 40 minutes ago -
How would you train your employees to avoid risks of using
mobile devices?
asked 1 hour ago -
Assume Kw = 1.01 ✕ 10−14
For pure water, we can calculate [H3O+ ] = [OH...
asked 2 hours ago -
Suppose that on a temperature scale X, water boils at 203.0°X
and freezes at -105.7°X. What...
asked 2 hours ago -
BaS crystallizes in a cubic unit cell with S2- ions on each
corner and each face....
asked 3 hours ago -
A. 0≤P(Oi)≤10≤P(Oi)≤1 for each i
B. P(Oi)≤0P(Oi)≤0
C. P(Oi)=1+P(OCi)P(Oi)=1+P(OiC)
D. P(Oi)≥1P(Oi)≥1
If an experiment consists of...
asked 4 hours ago -
A battery has an emf of 9.20V and an internal resistance of 1.20
ohm. a)What resistance...
asked 4 hours ago -
The area of an elastic circular loop decreases at a constant
rate, dA/dt = −6.60×10−3 m2/s...
asked 5 hours ago -
The denaturation of proteins can be described by the
equilibrium
F⇌U
where F and U represent...
asked 7 hours ago -
Please answer what the maximum and minimum force is, and the
angle on the ion is...
asked 7 hours ago -
implement a program that reads a number of rows and a symbol.
The program will draw...
asked 7 hours ago -
Assume that when adults with smartphones are randomly selected,
45% use them in meetings or classes....
asked 7 hours ago