1. Solve the following ODE's using the Trial Solution Method. This method is also know as...
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...
SOLVE USING MATLAB ONLY AND SHOW FULL CODE. PLEASE TO SHOW TEXT BOOK SOLUTION. SOLVE PART D ONLY Apply Euler's Method with step sizes h # 0.1 and h 0.01 to the initial value problems in Exercise 1. Plot the approximate solutions and the correct solution on [O, 1], and find the global truncation error at t-1. Is the reduction in error for h -0.01 consistent with the order of Euler's Method? REFERENCE: Apply the Euler's Method with step size...
Please show Matlab code and Simulink screenshots 2. Differential Equation (5 points) Using (i) Euler's method and (ii) modified Euler's method, both with step size h-0.01, to construct an approximate solution from t-0 to t-2 for xt 2 , 42 with initial condition x(0)-1. Compare both results by plotting them in the same figure. 3. Simulink (5 points) Solve the above differential equation using simplink. Present the model and result. 2. Differential Equation (5 points) Using (i) Euler's method and...
Using MATLAB_R2017a, solve #3 using the differential equation in question #2 using Simulink, present the model and result. 2. Differential Equation (5 points) Using (i) Euler's method and (ii) modified Euler's method, both with step size h-0.01, to construct an approximate solution from F0 to F2 for xt 2, 42 with initial condition x(0)=1. Compare both results by plotting them in the same figure. 3. Simulink (5 points) Solve the above differential equation using simplink. Present the model and result....
MATLAB CODE: Task 2 8y dt Solve the above ordinary differential equation (ODE) using Euler's method with step sizes of: 2. h 0.75 3. h 0.5 4. h 0.001 a) For each step size, plot the results at each step starting from y(0) 3 to y(3). b) Plot on the same figure as part a) the analytical solution which is given by: 9 24 -8t c) Calculate and print the percentage error between the Euler's method and the analytical result...
Find an approximate solution to the pendulum problem such that d2 theta /dt2 +g/l theta = 0. Use an approximate solver in matlab to find the solution to the exact equation d2 theta/dt2 +g/l * sin( theta) = 0. Compare the two solutions when the initial angle is 10, 30, and 90. Find a way to quantify the difference. One approximate method for solving differential equations is Runge-Kutta, which in Matlab goes by the name ode45. I have made a...
4. * Using your calculations from 3., plot the exact solution to dy = 1-y, dt y(0) = 1/2, for 0 <ts1, along with the numerical solution given by Euler's method and the trapezoid method, both with stepsize h = 0.1. Give the approximation of y(t = 1) for each numerical method. To distinguish your solutions: (i) Plot the Euler solution using crosses; do not join them with line segments. (ii) Plot the trapezoid solution using squares; again do not...
Read each of the following questions and answer them carefully. Show all of your work and label your answers clearly. 1. Classify the following ODEs. Include the order, homogeneous or hon-homogeneous, linear or non-linear, and also state the independent and dependent vari- ables. 4+12029 2. Solve the following ODE's using the Trial Solution Method. This method is also know as the Classical Solution Technique. Initial Conditions are given for each equation.
solve with matlab FOUR-Matlab Solve the following equation of motion using Matlab ODE45: 4 -m 6(0) 6(0)-0.1 (0) 0.2 0(0)-1 Assume that: m-0.1 kg, g-10 m/s, L-1 m, r-0.5 m. Plot θ vs 1 and θ vs θ FOUR-Matlab Solve the following equation of motion using Matlab ODE45: 4 -m 6(0) 6(0)-0.1 (0) 0.2 0(0)-1 Assume that: m-0.1 kg, g-10 m/s, L-1 m, r-0.5 m. Plot θ vs 1 and θ vs θ