Numerical analysis Given the initial value problem y '= 2y + t-1, with y(0) = 1, applying a step of the modified Euler method with step size h> 0 gives an approximation y1 = 3/2 to y( h). Find the value of h.
Added by Jill R.
Step 1
Modified Euler method formula: \[y_n = y_{n-1} + \frac{h}{2} \left( f(t_{n-1}, y_{n-1}) + f(t_n, y_n^*) \right)\] where \(y_n^* = y_{n-1} + hf(t_{n-1}, y_{n-1})\). ** Show more…
Show all steps
Close
Your feedback will help us improve your experience
Ishana K and 89 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Show that when Euler's method is used to approximate the solution of the initial value problem $$y ^ { \prime } = - \frac { 1 } { 2 } y , \quad y ( 0 ) = 3$$ at $$x = 2$$, then the approximation with step size h is $$3 \left( 1 - \frac { h } { 2 } \right) ^ { 2 / h }$$.
Mathematical Models and Numerical Methods Involving First-Order Equations
Numerical Methods: A Closer Look At Euler's Algorithm
use Euler s Method to approximate the given value of $y(t)$ with the time step h indicated.$$ y(0.7) ; \quad \dot{y}=2 y, \quad y(0)=3, \quad h=0.1 $$
INTRODUCTION TO DIFFERENTIAL EQUATIONS
Graphical and Numerical Methods
Use Euler's method with step size $h=0.2$ to approximate the solution to the initial value problem $y^{\prime}=\frac{1}{x}\left(y^{2}+y\right), \quad y(1)=1$ at the points $x=1.2,1.4,1.6,$ and $1.8 .$
Introduction
The Approximation Method of Euler
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD