Consider the IVP,
1. Apply the FEUT to show that a solution exists.
2. Use the Runge-Kutta method with various step-sizes to estimate
the maximum t-value, t=t∗>0, for which the solution is defined
on the interval [0,t∗). Include a few representative graphs with
your submission, but not the lists of points.
3. Find the exact solution to the IVP and solve for t∗
analytically. How close was your approximation from the previous
question?
4. The Runge-Kutta method continues to give data for t>t∗. Does
this data have any meaning or significance? Explain.
MATLAB, Excel, or C++ graphs are acceptable.
Homework Answers
Add Answer to:
Consider the IVP,
1. Apply the FEUT to show that a solution exists.
2. Use the...
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...
Numerical Methods Consider the following IVP dy=0.01(70-y)(50-y), with y(0)-0 (a) [10 marks Use the Runge-Kutta method of order four to obtain an approximate solution to the ODE at the points t-0.5 an...
Numerical Methods
Consider the following IVP dy=0.01(70-y)(50-y), with y(0)-0 (a) [10 marks Use the Runge-Kutta method of order four to obtain an approximate solution to the ODE at the points t-0.5 and t1 with a step sizeh 0.5. b) [8 marks Find the exact solution analytically. (c) 7 marks] Use MATLAB to plot the graph of the true and approximate solutions in one figure over the interval [.201. Display graphically the true errors after each steps of calculations.
Consider the...
Complete using MatLab 1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's...
Complete using MatLab
1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's Method and the second order Runge-Kutta method, for t E [0, 1] with a step size of h 0.05, approximate the solution to the initial value problem. Plot the true solution and the approximate solutions on the same figure. Be sure to label your axis and include an a. appropriate legend b. Verify that the analytic solution to the differential equation is given by...
Problem 1 Use Euler's method with step size h = 0.5 to approximate the solution of the IVP. 2 dy ...
Problem 1 Use Euler's method with step size h = 0.5 to approximate the solution of the IVP. 2 dy ev dt t 1-t-2, y(1) = 0. Problem 2 Consider the IVP: dy dt (a) Use Euler's method with step size h0.25 to approximate y(0.5) b) Find the exact solution of the IV P c) Find the maximum error in approximating y(0.5) by y2 (d) Calculate the actual absolute error in approximating y(0.5) by /2.
Problem 1 Use Euler's method...
step Consider the IVP y = 1 + y?, y(0) = 0 a. Use the Runge-Kutta...
step Consider the IVP y = 1 + y?, y(0) = 0 a. Use the Runge-Kutta Method with step size 0.1 to approximate y(0.2) b. Find the error between the analytic solution and the approximate solution at each step
Matlab & Differential Equations Help Needed I need help with this Matlab project for differential equations. I've got 0 experience with Matlab other than a much easier project I did in another...
Matlab & Differential Equations Help Needed
I need help with this Matlab project for differential equations.
I've got 0 experience with Matlab other than a much easier project
I did in another class a few semesters ago. All we've been given is
this piece of paper and some sample code. I don't even know how to
begin to approach this. I don't know how to use Matlab at all and I
barely can do this material.
Here's the handout:
Here's...
Use the Runge Kutta 4th Order (RK-4) Method on the function below to predict the value...
Use the Runge Kutta 4th Order (RK-4) Method on the function below to predict the value of y(0.1), given t = 0, y(0)-2, and h-01. Report your answer to 3 decimal places. dy/dt = e + 3y Answer: Use the Runge-Kutta 4th Order (RK-4) Method on the function below to predict the value of y(0.2), given y(0.1) from the previous question, and h = 0.1. Report your answer to 3 decimal places. -t dy/dt -e +3y Answer
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.
Differential Equations with MATLAB/Plotting first order differential equations in Matlab/ Differential Equations MATLAB/IVP Matlab/IVP I'd really...
Differential Equations with MATLAB/Plotting first order
differential equations in Matlab/ Differential Equations MATLAB/IVP
Matlab/IVP
I'd really appreciate if I can get some help plotting these 3
first order differential equations as well as their comments.
PLEASE! ANYTHING HELPS, I am very stuck :(
EZplot and ODE 45 were mentioned in class and the instructions
in class were not clear at all.
Given the first order differential equation with initial condition. dy/dt = y t, y(0)=-1 Complete problems 1-3 in one...
Please solve this problem by hand calculation. Thanks Consider the following system of two ODES: dx = x-yt dt dy = t+ y...
Please solve this problem by hand calculation. Thanks
Consider the following system of two ODES: dx = x-yt dt dy = t+ y from t=0 to t = 1.2 with x(0) = 1, and y(0) = 1 dt (a) Solve with Euler's explicit method using h = 0.4 (b) Solve with the classical fourth-order Runge-Kutta method using h = 0.4. The a solution of the system is x = 4et- 12et- t2 - 3t - 3, y= 2et- t-1. In...
Numerical Methods
Consider the following IVP dy=0.01(70-y)(50-y), with y(0)-0 (a) [10 marks Use the Runge-Kutta method of order four to obtain an approximate solution to the ODE at the points t-0.5 and t1 with a step sizeh 0.5. b) [8 marks Find the exact solution analytically. (c) 7 marks] Use MATLAB to plot the graph of the true and approximate solutions in one figure over the interval [.201. Display graphically the true errors after each steps of calculations.
Consider the...
Complete using MatLab
1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's Method and the second order Runge-Kutta method, for t E [0, 1] with a step size of h 0.05, approximate the solution to the initial value problem. Plot the true solution and the approximate solutions on the same figure. Be sure to label your axis and include an a. appropriate legend b. Verify that the analytic solution to the differential equation is given by...
Problem 1 Use Euler's method with step size h = 0.5 to approximate the solution of the IVP. 2 dy ev dt t 1-t-2, y(1) = 0. Problem 2 Consider the IVP: dy dt (a) Use Euler's method with step size h0.25 to approximate y(0.5) b) Find the exact solution of the IV P c) Find the maximum error in approximating y(0.5) by y2 (d) Calculate the actual absolute error in approximating y(0.5) by /2.
Problem 1 Use Euler's method...
step Consider the IVP y = 1 + y?, y(0) = 0 a. Use the Runge-Kutta Method with step size 0.1 to approximate y(0.2) b. Find the error between the analytic solution and the approximate solution at each step
Matlab & Differential Equations Help Needed
I need help with this Matlab project for differential equations.
I've got 0 experience with Matlab other than a much easier project
I did in another class a few semesters ago. All we've been given is
this piece of paper and some sample code. I don't even know how to
begin to approach this. I don't know how to use Matlab at all and I
barely can do this material.
Here's the handout:
Here's...
Use the Runge Kutta 4th Order (RK-4) Method on the function below to predict the value of y(0.1), given t = 0, y(0)-2, and h-01. Report your answer to 3 decimal places. dy/dt = e + 3y Answer: Use the Runge-Kutta 4th Order (RK-4) Method on the function below to predict the value of y(0.2), given y(0.1) from the previous question, and h = 0.1. Report your answer to 3 decimal places. -t dy/dt -e +3y Answer
Differential Equations with MATLAB/Plotting first order
differential equations in Matlab/ Differential Equations MATLAB/IVP
Matlab/IVP
I'd really appreciate if I can get some help plotting these 3
first order differential equations as well as their comments.
PLEASE! ANYTHING HELPS, I am very stuck :(
EZplot and ODE 45 were mentioned in class and the instructions
in class were not clear at all.
Given the first order differential equation with initial condition. dy/dt = y t, y(0)=-1 Complete problems 1-3 in one...
Please solve this problem by hand calculation. Thanks
Consider the following system of two ODES: dx = x-yt dt dy = t+ y from t=0 to t = 1.2 with x(0) = 1, and y(0) = 1 dt (a) Solve with Euler's explicit method using h = 0.4 (b) Solve with the classical fourth-order Runge-Kutta method using h = 0.4. The a solution of the system is x = 4et- 12et- t2 - 3t - 3, y= 2et- t-1. In...
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