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Consider the following first-order ODE which represents the rate of formation of compound y: dy dt Зу = t from t = 1 to t = 2.2 with y(1) = 1 t dy 3y t² from t1 to t = 2.2 with y(1) = 1 dt t a.) Solve the ODE with the 2nd Order Runge- Kutta Method (Midpoint Version) using a step size of h = 0.3. b.) The analytical solution of the ODE in part a.) above is: y 1/5 =증(+3) 6 y 1/5 == +t3 6 3 In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined Runge-Kutta Method (Modified Euler version) Xi+1 = Xi th K₁ = f(xi, yi) K₂ = f(x¡ + h, y₁ + K₁h) 1 Yi+1 = Yi + (K₁ + K₂)h z

Consider the following first-order ODE which represents the rate of formation of compound y: dy dt Зу = t from t = 1 to t = 2.2 with y(1) = 1 t dy 3y t² from t1 to t = 2.2 with y(1) = 1 dt t a.) Solve the ODE with the 2nd Order Runge- Kutta Method (Midpoint Version) using a step size of h = 0.3. b.) The analytical solution of the ODE in part a.) above is: y 1/5 =증(+3) 6 y 1/5 == +t3 6 3 In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined Runge-Kutta Method (Modified Euler version) Xi+1 = Xi th K₁ = f(xi, yi) K₂ = f(x¡ + h, y₁ + K₁h) 1 Yi+1 = Yi + (K₁ + K₂)h z

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Consider the following first-order ODE which represents the rate of formation of compound y: dy dt Зу = t from t = 1 to t = 2.2 with y(1) = 1 t dy 3y t² from t1 to t = 2.2 with y(1) = 1 dt t a.) Solve the ODE with the 2nd Order Runge- Kutta Method (Midpoint Version) using a step size of h = 0.3. b.) The analytical solution of the ODE in part a.) above is: y 1/5 =증(+3) 6 y 1/5 == +t3 6 3 In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined Runge-Kutta Method (Modified Euler version) Xi+1 = Xi th K₁ = f(xi, yi) K₂ = f(x¡ + h, y₁ + K₁h) 1 Yi+1 = Yi + (K₁ + K₂)h z
Transcribed Image Text:Consider the following first-order ODE which represents the rate of formation of compound y: dy dt Зу = t from t = 1 to t = 2.2 with y(1) = 1 t dy 3y t² from t1 to t = 2.2 with y(1) = 1 dt t a.) Solve the ODE with the 2nd Order Runge- Kutta Method (Midpoint Version) using a step size of h = 0.3. b.) The analytical solution of the ODE in part a.) above is: y 1/5 =증(+3) 6 y 1/5 == +t3 6 3 In each part, calculate the error between the true solution and the numerical solution at the points where the numerical solution is determined Runge-Kutta Method (Modified Euler version) Xi+1 = Xi th K₁ = f(xi, yi) K₂ = f(x¡ + h, y₁ + K₁h) 1 Yi+1 = Yi + (K₁ + K₂)h z
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