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Using a PYTHON code solve dy dt over the interval 0 ≤ t ≤ 2, with a step size of 0.5 implementing (i) Euler's method, (ii) midpoint method (iii) built-in solve_ivp Print the results for y(2) for analytical solution (given below) and the three different methods. Also display the results from all three methods on the same figure along with the analytical result. Use continuous plot for the analytical solution and discrete plots for the different methods. Use proper legend Given analytical solution, y(t) = ²/(t² +t+ 2)² = (1 + 2t) √y, y (0) = 1

Using a PYTHON code solve dy dt over the interval 0 ≤ t ≤ 2, with a step size of 0.5 implementing (i) Euler's method, (ii) midpoint method (iii) built-in solve_ivp Print the results for y(2) for analytical solution (given below) and the three different methods. Also display the results from all three methods on the same figure along with the analytical result. Use continuous plot for the analytical solution and discrete plots for the different methods. Use proper legend Given analytical solution, y(t) = ²/(t² +t+ 2)² = (1 + 2t) √y, y (0) = 1

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Using a PYTHON code solve dy = (1 + 2t)√y, y (0) = 1 dt over the interval 0 ≤ t ≤ 2, with a step size of 0.5 implementing (i) Euler's method, (ii) midpoint method (iii) built-in solve_ivp Print the results for y(2) for analytical solution (given below) and the three different methods. Also display the results from all three methods on the same figure along with the analytical result. Use continuous plot for the analytical solution and discrete plots for the different methods. Use proper legend. Given analytical solution, y(t) = 1/(t² +t+ 2)² 4
Transcribed Image Text:Using a PYTHON code solve dy = (1 + 2t)√y, y (0) = 1 dt over the interval 0 ≤ t ≤ 2, with a step size of 0.5 implementing (i) Euler's method, (ii) midpoint method (iii) built-in solve_ivp Print the results for y(2) for analytical solution (given below) and the three different methods. Also display the results from all three methods on the same figure along with the analytical result. Use continuous plot for the analytical solution and discrete plots for the different methods. Use proper legend. Given analytical solution, y(t) = 1/(t² +t+ 2)² 4
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