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Solve the following initial value problem by hand calculation over the interval from t = 0 to t = 2 using the two specified methods. The initial condition is y(0) = 1. dy dt = t²y — 1.1y - The analytic solution to this ODE is y(t) = exp(t³/3- 1.1t). For both solution methods below, make a table of the numerical solution values, the analytic solution values and the percentage error between the numerical and analytic solution at t = 0.5, 1, 1.5. Define the percentage error as follows: Ynum Yanalytic % error = × 100 Yanalytic (a) Using Euler's method with h = 0.5 and h = 0.25. (b) Using the midpoint method with h = 0.5

Solve the following initial value problem by hand calculation over the interval from t = 0 to t = 2 using the two specified methods. The initial condition is y(0) = 1. dy dt = t²y — 1.1y - The analytic solution to this ODE is y(t) = exp(t³/3- 1.1t). For both solution methods below, make a table of the numerical solution values, the analytic solution values and the percentage error between the numerical and analytic solution at t = 0.5, 1, 1.5. Define the percentage error as follows: Ynum Yanalytic % error = × 100 Yanalytic (a) Using Euler's method with h = 0.5 and h = 0.25. (b) Using the midpoint method with h = 0.5

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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Solve the following initial value problem by hand calculation over the interval from t = 0 to t = 2 using the two specified methods. The initial condition is y(0) = 1. dy dt = t²y — 1.1y - The analytic solution to this ODE is y(t) = exp(t³/3- 1.1t). For both solution methods below, make a table of the numerical solution values, the analytic solution values and the percentage error between the numerical and analytic solution at t = 0.5, 1, 1.5. Define the percentage error as follows: Ynum Yanalytic % error = × 100 Yanalytic (a) Using Euler's method with h = 0.5 and h = 0.25. (b) Using the midpoint method with h = 0.5
Transcribed Image Text:Solve the following initial value problem by hand calculation over the interval from t = 0 to t = 2 using the two specified methods. The initial condition is y(0) = 1. dy dt = t²y — 1.1y - The analytic solution to this ODE is y(t) = exp(t³/3- 1.1t). For both solution methods below, make a table of the numerical solution values, the analytic solution values and the percentage error between the numerical and analytic solution at t = 0.5, 1, 1.5. Define the percentage error as follows: Ynum Yanalytic % error = × 100 Yanalytic (a) Using Euler's method with h = 0.5 and h = 0.25. (b) Using the midpoint method with h = 0.5
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