Homework Answers
Question 21:
Correct option:
Heun
Explanation:
Heun's method for the solution of Ordinary Differential Equation assumes the slope as the average of slopes at the beginning and the end of the interval.
Question 22:
In general, decreasing the step size, h, will decrease the error in a numerical approximation of a drivative.
Explanation:
The derivative of f(x) can be written using Taylor expansion as follows:
From this equation, we conclude: , decreasing the step size, h, will decrease the error in a numerical approximation of a drivative.
Add Answer to:
Question 21 2 pts Which of the following is based on using the average of two...
Question 19 2 pts In the following ODE, y is the independent variable. dy der 5ytet...
Question 19 2 pts In the following ODE, y is the independent variable. dy der 5ytet True O False Question 20 2 pts Which of the following is the simplest Runge-Kutta method? Euler Heun O Midpoint Ralston
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial...
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial value problem G.EE +15y = 1.C:y(0) - 0.5 Carry out a single step of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.2, and the predicted solutions is Y(0.2)-0.20 None of the above y(0.2)-1.27 Y(0.2)-0.25 (0.2)--0.75
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial...
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first...
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first derivative using, 2, 3, and 4 points for the function y = cos x at x = 7/4 using step size h = /12. Provide the results in the hard copy. Note that the central differences can only be apply for odd number of points ). b. Provide the analytic form of the derivatives, as well as table of the computed relative error for...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equat...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
4. (25 points) Solve the following ODE using classical 4th-order Runge- Kutta method within the domain...
4. (25 points) Solve the following ODE using classical 4th-order Runge- Kutta method within the domain of x = 0 to x= 2 with step size h = 1: dy 3 dr=y+ 6x3 dx The initial condition is y(0) = 1. If the analytical solution of the ODE is y = 21.97x - 5.15; calculate the error between true solution and numerical solution at y(1) and y(2).
(PLEASE COMPLETE EACH PART OF THE QUESTION , WITH FULL WORKING THANK YOU) QUESTION 4 Consider a car driving along a roa...
(PLEASE COMPLETE EACH PART OF THE QUESTION , WITH FULL
WORKING THANK YOU)
QUESTION 4 Consider a car driving along a road, which has a traction force and a drag force acting on it. We can model the car with the ODE v'(t) m where v(t) is the velocity of the car, F, is the traction force and k is a drag coefficient. Given m 1000, Fi = 10000e, k 0.5 and v(0) 0, 13.63 (a) Use Euler's Method to...
Please show me the steps to solve this problem using both backward and forward Euler Question...
Please show me the steps to solve this problem using both
backward and forward Euler
Question 44 4/4 pts Given the ODE with initial condition x' (t) = 3x +t, «(1) = 2 We solve it with implicit backward Euler method, using time step h=0.1. What is the approximate solution for x(1.1)? 2.8745 0 3.62 3.0143 0 2.7
Question 22 1 pts Problem 22: Numerical solution of Ordinary differential equations Consider the following initial...
Question 22 1 pts Problem 22: Numerical solution of Ordinary differential equations Consider the following initial value problem GE:+15y = 1.C:y(0) -0.5 Carry out two-steps of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.1. and the predicted solutions is y(0.2)-0.20 None of the above. y(0.2) - -0.75 y(0.2)-1.27 y(0.2)=0.25
Question 2. Consider the approximation of the definite integral () (a) Begin by using 2 points/nodes...
Question 2. Consider the approximation of the definite integral () (a) Begin by using 2 points/nodes (i.e., n + 1 = 2, with the two points being x = a and r = b). Replace f(x) by the constant /(a+b)/2] on the entire interval a <<b. Show that this leads to the numerical integration formula M,()) = (b − a) ) Graphically illustrate this approximation. (b) In analogy with the derivation of the Trapezoidal rule and Simpson's rule, generalize part...
Question 19 2 pts In the following ODE, y is the independent variable. dy der 5ytet True O False Question 20 2 pts Which of the following is the simplest Runge-Kutta method? Euler Heun O Midpoint Ralston
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial value problem G.EE +15y = 1.C:y(0) - 0.5 Carry out a single step of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.2, and the predicted solutions is Y(0.2)-0.20 None of the above y(0.2)-1.27 Y(0.2)-0.25 (0.2)--0.75
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first derivative using, 2, 3, and 4 points for the function y = cos x at x = 7/4 using step size h = /12. Provide the results in the hard copy. Note that the central differences can only be apply for odd number of points ). b. Provide the analytic form of the derivatives, as well as table of the computed relative error for...
Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equation numerically over the interval 0 s i s 2.0 and a step size h At 0.5.A Apply the following Runge-Kutta methods for each of the step. (show your calculations) i. [0.0 0.5: Euler method ii. [0.5 1.0]: Heun method. ii. [1.0 1.5): Midpoint method. iv. [1.5 2.0): 4h RK method...
4. (25 points) Solve the following ODE using classical 4th-order Runge- Kutta method within the domain of x = 0 to x= 2 with step size h = 1: dy 3 dr=y+ 6x3 dx The initial condition is y(0) = 1. If the analytical solution of the ODE is y = 21.97x - 5.15; calculate the error between true solution and numerical solution at y(1) and y(2).
(PLEASE COMPLETE EACH PART OF THE QUESTION , WITH FULL
WORKING THANK YOU)
QUESTION 4 Consider a car driving along a road, which has a traction force and a drag force acting on it. We can model the car with the ODE v'(t) m where v(t) is the velocity of the car, F, is the traction force and k is a drag coefficient. Given m 1000, Fi = 10000e, k 0.5 and v(0) 0, 13.63 (a) Use Euler's Method to...
Please show me the steps to solve this problem using both
backward and forward Euler
Question 44 4/4 pts Given the ODE with initial condition x' (t) = 3x +t, «(1) = 2 We solve it with implicit backward Euler method, using time step h=0.1. What is the approximate solution for x(1.1)? 2.8745 0 3.62 3.0143 0 2.7
Question 22 1 pts Problem 22: Numerical solution of Ordinary differential equations Consider the following initial value problem GE:+15y = 1.C:y(0) -0.5 Carry out two-steps of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.1. and the predicted solutions is y(0.2)-0.20 None of the above. y(0.2) - -0.75 y(0.2)-1.27 y(0.2)=0.25
Question 2. Consider the approximation of the definite integral () (a) Begin by using 2 points/nodes (i.e., n + 1 = 2, with the two points being x = a and r = b). Replace f(x) by the constant /(a+b)/2] on the entire interval a <<b. Show that this leads to the numerical integration formula M,()) = (b − a) ) Graphically illustrate this approximation. (b) In analogy with the derivation of the Trapezoidal rule and Simpson's rule, generalize part...
Most questions answered within 3 hours.
-
An AC generator supplies an rms voltage of 240 V at 50.0 Hz. It
is connected...
asked 51 seconds ago -
China’s income per capital maintained an 8% rate of growth in
recent decades. As a result,...
asked 4 minutes ago -
Journalize the entries to record the following (refer to the
Chart of Accounts for exact wording...
asked 2 minutes ago -
What steps would you take to institutionalize the controls you’d
select for your organization? Where do...
asked 18 minutes ago -
Learning aquatic zumba is an example of tacit knowledge. true or
false
asked 19 minutes ago -
Table salt contains 39.33 g of sodium per 100 g of salt. The
U.S. Food and...
asked 36 minutes ago -
C&A records the following profit figures for the last six
months in Excel for a linear...
asked 33 minutes ago -
This needs to be done in c++11 and be compatible with g++
compiling
Project description:
Write...
asked 34 minutes ago -
.
NEED ANSWER ASAP
******NEW ANSWER NEVER USED BEFORE****
Write a page paper on conducting marketing...
asked 36 minutes ago -
Assume that capital markets are competitive and that the
international Fisher hypothesis holds. The one-year interest...
asked 1 hour ago -
Solid potassium phosphate is slowly added to 150 mL of a 0.0518
M calcium nitrate solution....
asked 1 hour ago -
(CO 2) A field can be added to a report to
values for two or more...
asked 3 hours ago