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Consider the ODE f(x, y) = x-5. Take initial conditions x = 0, yo = y(0) = 11, x₁ = 0.2 and y₁ = y(0.2) = 22, solve for y(99) 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: + h ( 1/2 f(x+· Yi+1) + f(x₁, y)) Yi+2=Yi+1 +h

Consider the ODE f(x, y) = x-5. Take initial conditions x = 0, yo = y(0) = 11, x₁ = 0.2 and y₁ = y(0.2) = 22, solve for y(99) 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: + h ( 1/2 f(x+· Yi+1) + f(x₁, y)) Yi+2=Yi+1 +h

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
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Consider the ODE f(x, y) = x-5. Take initial conditions x = 0, yo = y(0) = 11, x₁ = 0.2 and y₁ = y(0.2) = 22, solve for y(99) 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: Yi+z = Yi+s + h ( 12 f(xi+n+Yi+s) + f(x, y)) An example of the first few iterations is shown below. Y₂ = ₁ + h ( 2 f(x₁+x₁) + f(xo. Yo ) - Ys = y₂ + h +1 ( 1 [ƒ(6×2,082) + f(x1, 85) ) = 19 f(x₂.y 20.9333 What is the value of y(99) rounded to the nearest integer? Note: Remember to round the final answer. 19.9100 34 = 95 + h (25(85.353) + ²56(62.92)) = 16 18.9300
Transcribed Image Text:Consider the ODE f(x, y) = x-5. Take initial conditions x = 0, yo = y(0) = 11, x₁ = 0.2 and y₁ = y(0.2) = 22, solve for y(99) 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: Yi+z = Yi+s + h ( 12 f(xi+n+Yi+s) + f(x, y)) An example of the first few iterations is shown below. Y₂ = ₁ + h ( 2 f(x₁+x₁) + f(xo. Yo ) - Ys = y₂ + h +1 ( 1 [ƒ(6×2,082) + f(x1, 85) ) = 19 f(x₂.y 20.9333 What is the value of y(99) rounded to the nearest integer? Note: Remember to round the final answer. 19.9100 34 = 95 + h (25(85.353) + ²56(62.92)) = 16 18.9300
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