Euler_Improved_Kutta - MAT 2384-Practice Problems on...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MAT 2384-Practice Problems on Numerical Methods for Differential Equations Question 1. For each of the Following IVP’s, apply Euler Method with the given step size h to estimate solutions on the given interval. Round your answers to 6 decimal places. Then Solve the IVP exactly and compare your estimations with the Exact values. 1. y + 5x4 y 2 = 0, y (0) = 1, h = 0.1 on [0, 0.5] 1 2. y = 2 π 1 − y 2 , y (0) = 0, h = 0.1 on [0, 0.3] 3. y = (y + x)2 , y (0) = 0, h = 0.1 on [0, 0.4] Question 2. For each of the Following IVP’s, apply the Improved Euler Method with the given step size h to estimate solutions on the given interval. Round your answers to 6 decimal places. Then Solve the IVP exactly and compare your estimations with the Exact values. 1. y = y − y 2 = 0, y (0) = 0.5, h = 0.1 on [0, 0.3] 2. y + 2xy 2 = 0, y (0) = 1, h = 0.2 on [0, 0.6] 3. y = 2(y 2 + 1), y (0) = 0, h = 0.05 on [0, 0.2] Question 3. Consider the IVP: y = 2x−1 y − ln x + x−1 , y (1) = 0. (1) Verify that the Exact solution is y = (ln x)2 + ln x (2) Use the Improved Euler Method to estimate solutions of the IVP on the interval 1 ≤ x ≤ 1.6 using a step size of h = 0.2. Round your answers to 6 decimal places (3) Use the Runge-Kutta method of order 4 to estimate solutions of the IVP on the interval 1 ≤ x ≤ 1.6 using a step size of h = 0.2. Round your answers to 6 decimal places 1 (4) Make a table to compare your estimates in parts (2) and (3) with the exact values (from part (1)). Question 4. Use the Runge-Kutta method of order 4 to estimate solutions of the IVP y = xy + cos x, y (0) = 0 on the interval 0 ≤ x ≤ 0.6 using a step size of h = 0.2. 2 ...
View Full Document

Page1 / 2

Euler_Improved_Kutta - MAT 2384-Practice Problems on...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online