Question

Use Euler's method with step sizes $h=0.1,0.02,0.004$, and $0.0008$ to approximate to four decimal places the values of the solution at ten equally spaced points of the given interval. Print the results in tabular form with appropriate headings to make it easy to gauge the effect of varying the step size h. Throughout, primes denote derivatives with respect to $x$. $$ y^{\prime}=\ln y, y(1)=2 ; 1 \leqq x \leqq 2 $$

          Use Euler's method with step sizes $h=0.1,0.02,0.004$, and $0.0008$ to approximate to four decimal places the values of the solution at ten equally spaced points of the given interval. Print the results in tabular form with appropriate headings to make it easy to gauge the effect of varying the step size h. Throughout, primes denote derivatives with respect to $x$.
$$
y^{\prime}=\ln y, y(1)=2 ; 1 \leqq x \leqq 2
$$

Added by Consuelo W.

Differential Equations and Linear Algebra

Stephen W. Goode, Scott A. Annin 4th Edition

Instant Answer

Solved by Expert Adi S

11/07/2023

Step 1

We have the differential equation $y' = \ln y$ and the initial condition $y(1) = 2$. Show more…

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Use Euler's method with step sizes $h=0.1,0.02,0.004$, and $0.0008$ to approximate to four decimal places the values of the solution at ten equally spaced points of the given interval. Print the results in tabular form with appropriate headings to make it easy to gauge the effect of varying the step size h. Throughout, primes denote derivatives with respect to $x$. $$ y'=ln y, y(1)=2 ; 1 leqq x leqq 2 $$