Consider the initial value problem given below.
y'=x+4cos(xy), Y(0)=0
Use the improved Euler's method subroutine with...
Consider the initial value problem given below.
y'=x+4cos(xy), Y(0)=0
Use the improved Euler's method subroutine with step size h=0.3
to approximate the solution to the initial value problem at points
x= 0.0,0.3,0.6.....3.0
Consider the initial value problem: y0 = 3 + x−y, y(0) = 1 (a)
Solve it analytically. (b) Solve it using Euler’s method using step
size h = 0.1 and find an approximation to true solution at x = 0.3.
(c) What is the error in the Euler’s method at x = 0.3
Euler’s method
Consider the initial-value problem y′ = −2y, y(0) = 1. The
analytic solution is y(x) = e−2x . (a) Approximate y(0.1) using one
step of Euler’s method. (b) Find a bound for the local truncation
error in y1 . (c) Compare the error in y1 with your error bound.
(d) Approximate y(0.1) using two steps of Euler’s method. (e)
Verify that the global truncation error for Euler’s method is O(h)
by comparing the errors in parts (a) and...
Use the improved 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' = y − y^2, y(0) = 0.8; y(0.5) y(0.5) ≈________ (h
= 0.1)
y(0.5) ≈ _________(h = 0.05)