Consider following initial value problem: dy where k 0.01, a 70 and b 50 and the exact solution is y(t) 350 1- exp(-0.21)] /[7-5 exp-0.2t)]. a) Verify that this is the solution, by substituting into the original differential equation. b) Use the method of separation of variables, to derive the solution. c) Write a MATLAB code to numerically solve the initial value problem over the interval [0, 20] using Euler's method with a fixed sample period, A 0.5. Calculate the error curve for the following sample periods Δ1-0.5, 0.2 and 0.1. d) Repeat part a) using Heun's method and the Runge-Kutta method.
Consider following initial value problem: dy where k 0.01, a 70 and b 50 and the exact solution is y(t) 350 1- exp(-0.21)] /[7-5 exp-0.2t)]. a) Verify that this is the solution, by substituting into the original differential equation. b) Use the method of separation of variables, to derive the solution. c) Write a MATLAB code to numerically solve the initial value problem over the interval [0, 20] using Euler's method with a fixed sample period, A 0.5. Calculate the error curve for the following sample periods Δ1-0.5, 0.2 and 0.1. d) Repeat part a) using Heun's method and the Runge-Kutta method.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider following initial value problem:
dy
where k 0.01, a 70 and b
50 and the exact solution is
y(t) 350 1- exp(-0.21)] /[7-5 exp-0.2t)].
a) Verify that this is the solution, by substituting into the original differential equation.
b) Use the method of separation of variables, to derive the solution.
c) Write a MATLAB code to numerically solve the initial value problem over the
interval [0, 20] using Euler's method with a fixed sample period, A 0.5. Calculate
the error curve for the following sample periods Δ1-0.5, 0.2 and 0.1.
d) Repeat part a) using Heun's method and the Runge-Kutta method.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19032c14-8ebf-499e-908d-47a126d342e4%2Ffad39ccb-6d81-47a0-972f-94c3fa96d24a%2Fzukscwv.png&w=3840&q=75)
Transcribed Image Text:Consider following initial value problem:
dy
where k 0.01, a 70 and b
50 and the exact solution is
y(t) 350 1- exp(-0.21)] /[7-5 exp-0.2t)].
a) Verify that this is the solution, by substituting into the original differential equation.
b) Use the method of separation of variables, to derive the solution.
c) Write a MATLAB code to numerically solve the initial value problem over the
interval [0, 20] using Euler's method with a fixed sample period, A 0.5. Calculate
the error curve for the following sample periods Δ1-0.5, 0.2 and 0.1.
d) Repeat part a) using Heun's method and the Runge-Kutta method.
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