Compute, by Euler’s method, an approximate solution to the
following initial value problem for h =...
Compute, by Euler’s method, an approximate solution to the
following initial value problem for h = 1/8 : y’ = t − y , y(0) = 2
; y(t) = 3e^(−t) + t − 1 . Find the maximum error over [0, 1]
interval.
Use eulers Method with step size h=.01 to approximate the
solution to the initial value problem y'=2x-y^2, y(6)=0 at the
points x=6.1, 6.2, 6.3, 6.4, 6.5
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 power series approximations method to approximate the
solution of the initial value problem: y"− (1+ x) y = 0 y(0) = 1
y'(0) = 2 (Write all the terms up to the power ). x^4
Plot the Euler’s Method approximate solution on [0,1] for the
differential equation
y* = 1 + y^2 and initial condition (a) y0 = 0 (b) y0 = 1, along
with the exact solution (see
Exercise 7). Use step sizes h = 0.1 and 0.05. The exact solution is
y = tan(t + c)
Use the method of Undetermined Coefficients to find the solution
of the initial value value problem:
y'' + 8y' + 20y = 9cos(2t) - 18e-4t, y(0) = 5. y'(0)
= 0
Determine the solution of the following initial boundary-value
problem using the method of separation of Variables
Uxx=4Utt 0<x<Pi t>0
U(x,0)=sinx 0<=x<Pi
Ut(x,0)=x 0<=x<Pi
U(0,t)=0 t>=0
U(pi,t)=0 t>=0
Calculate the Euler method approximation to the solution of the
initial value problem at the given x-values. Compare your results
to the exact solution at these x-values.
y' = y+y^2; y(1) = -1, x = 1.2, 1.4, 1.6, 1.8