Use Euler's method to approximate y(1.8). Start with step size h=0.1, and then use successively smaller step sizes (h=0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.8 agree rounded off to two decimalplaces.y'=x² + y²-2. y(0) = 0The approximate solution values at x = 1.8 begin to agree rounded off to two decimal places between(Type an integer or decimal rounded to two decimal places as needed.)▾ So, a good approximation of y(1.8) is.

Consider the given equation.And,The Euler formula is defined as.

Answered: Use Euler's method to approximate…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = x2 + y?, y(0) = 2; y(0.5) y(0.5) = (h = 0.1) y(0.5) = (h = 0.05) %D
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