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Consider the ODE ƒ(x, y) = x – y. Take initial conditions x, = 0, yo = y(0) = 11, x1 = 0.2 and y1 = y(0.2) = 2 solve for y(30) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions approximate the next y solution. The general formula is: Yi+2 = Yi+1 +h An example of the first few iterations is shown below. y2 = yı = 16.5600 y3 = Y2 + hf(x2, y½) (x1, Yı) = 13.8920 (3 = 11.5204

Consider the ODE ƒ(x, y) = x – y. Take initial conditions x, = 0, yo = y(0) = 11, x1 = 0.2 and y1 = y(0.2) = 2 solve for y(30) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions approximate the next y solution. The general formula is: Yi+2 = Yi+1 +h An example of the first few iterations is shown below. y2 = yı = 16.5600 y3 = Y2 + hf(x2, y½) (x1, Yı) = 13.8920 (3 = 11.5204

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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Consider the ODE ƒ(x,y) = x – y. Take initial conditions xo = 0, Yo = y(0) = 11, x1 solve for y(30) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to approximate the next y solution. The general formula is: = 0.2 and y, = y(0.2) = 22, 1 Yi+2 = Yi+1 +h An example of the first few iterations is shown below. Y2 = y1 + h = 16.5600 Y3 = y2 + h = 13.8920 Y4 = y3 +h = 11.5204 What is the value of y(30) rounded to the nearest integer? Note: Remember to round the final answer.
Transcribed Image Text:Consider the ODE ƒ(x,y) = x – y. Take initial conditions xo = 0, Yo = y(0) = 11, x1 solve for y(30) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to approximate the next y solution. The general formula is: = 0.2 and y, = y(0.2) = 22, 1 Yi+2 = Yi+1 +h An example of the first few iterations is shown below. Y2 = y1 + h = 16.5600 Y3 = y2 + h = 13.8920 Y4 = y3 +h = 11.5204 What is the value of y(30) rounded to the nearest integer? Note: Remember to round the final answer.
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