Please provide work and summary as well. Ill upvote if answer is satisfactory. Solving all except the 4th part will be s
Posted: Wed May 11, 2022 10:32 am
Please provide work and summary as well. Ill upvote if answer is
satisfactory.
Solving all except the 4th part will be satisfactory
1. (50+ points) The function y(t) = t Int + 2t is a solution to the Initial Value Problem (IVP) y y'= 4 =1+ y(1) = 2 - 2 / 2 ) t on the interval (0,00). (a.) (10 points) Is there a unique solution to the IVP on [1, 2]? Justify your answer. Recall that a correct answer without supporting work may not receive full credit. (6.) (15 points) What is the largest open interval on which there is a unique solution to the IVP? Justify your answer. Recall that a correct answer without supporting work may not receive full credit. (c.) (5 points) Run RK4 with h = 0.1. What are the first three terms (starting with the coefficient of ") of the Newton polynomial that passes through all points generated via RK4? (d.) (5 points) Plot the polynomial you obtained in the previous item and y(t) = t Int+ 2t in the same graph. (e.) (5 points) Approximate y(1.2) using Euler's Method with h = 0.1. (f.) (5 points) What is the relative error in the previous item? (9.) (5 points) Approximate y(1.2) using Euler's Method with h not fixed (your solution is written in terms of h). (h.) (5 points) What is the relative error in the previous item? (i.) (10 points) Give an example of h and n we can choose so that the relative error from the previous item is smaller than 0.01 (which means < 1%).
satisfactory.
- Please Provide Work And Summary As Well Ill Upvote If Answer Is Satisfactory Solving All Except The 4th Part Will Be S 1 (94.97 KiB) Viewed 36 times
1. (50+ points) The function y(t) = t Int + 2t is a solution to the Initial Value Problem (IVP) y y'= 4 =1+ y(1) = 2 - 2 / 2 ) t on the interval (0,00). (a.) (10 points) Is there a unique solution to the IVP on [1, 2]? Justify your answer. Recall that a correct answer without supporting work may not receive full credit. (6.) (15 points) What is the largest open interval on which there is a unique solution to the IVP? Justify your answer. Recall that a correct answer without supporting work may not receive full credit. (c.) (5 points) Run RK4 with h = 0.1. What are the first three terms (starting with the coefficient of ") of the Newton polynomial that passes through all points generated via RK4? (d.) (5 points) Plot the polynomial you obtained in the previous item and y(t) = t Int+ 2t in the same graph. (e.) (5 points) Approximate y(1.2) using Euler's Method with h = 0.1. (f.) (5 points) What is the relative error in the previous item? (9.) (5 points) Approximate y(1.2) using Euler's Method with h not fixed (your solution is written in terms of h). (h.) (5 points) What is the relative error in the previous item? (i.) (10 points) Give an example of h and n we can choose so that the relative error from the previous item is smaller than 0.01 (which means < 1%).