The boundary value problem y" (x) – a²y(x)= 0, y'(0) = 1, y(3) = 2 is discretized using central differences with step h = 1. Give the coordinate of the fictitious grid point z (enter integer value) . Determine the values of the solution at I = 0, x = 1 and z = 2: y (0) : Y(1) = y(2) . Round the answer to the fourth decimal place (Hint: You may proceed as in Q2 and Q3 of tutorial 7. Also note that by default, Matlab rounds the answer to the fourth decimal place). Now use the for loop to write a Matlab code that solves the above boundary value problem for arbitrary discretization step h. Use h = 0.1to determine the solution at z = 0 (Round the answer to the fourth decimal place).
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![The boundary value problem y" (x) – x²y(x)=0, y'(0) =1, y(3) = 2 is discretized using central differences with step h = 1.
Give the coordinate of the fictitious grid point I =
(enter integer value). Determine the values of the solution at
I = 0, x = 1 and z = 2: y (0) =
, y(1) =
y(2) =
Round the answer
to the fourth decimal place (Hint: You may proceed as in Q2 and Q3 of tutorial 7. Also note that by default, Matlab rounds the answer
to the fourth decimal place).
Now use the for loop to write a Matlab code that solves the above boundary value problem for arbitrary discretization step h. Use
h = 0.1to determine the solution at a
(Round the answer to the fourth decimal place).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb6a9708-e09f-4828-b8c7-39fbe4407ad9%2Feaf21460-3d6f-46b3-8b7c-5538ea76bd48%2Fdf83iyx_processed.png&w=3840&q=75)
![• The initial value problem y/ =
cos (ry), y(1) = 2 is to be solved on the interval z E [1,3] using the forward Euler
method with step h = 0.02 How many steps of the method must be taken to obtain the solution at z = 3?
Determine the value of the approximate solution at z = 3. Round correct to the fourth decimal place y(3) :
(Hint: By default Matlab rounds the answer to the fourth decimal place).
dr
dt
• The initial value problem
, z(0) = 1, y(0) = –-lis to be solved on the interval t e [0, 1] using the
3
In+1
backward Euler method with step h = 0.05 The iteration update rule for the method is | = (I – hA)
hA)-
Yn 41] =
(round to the fourth decimal place)
where I
Yn +1
is a 2 x 2 identity matrix. Determine the approximate values of ¤(1) =
and y(1) =
(round to the fourth decimal place). Now use the Matlab solver ode45 to obtain the solution at
t = 1: #(1) =
(round to the fourth decimal place) and y(1)
|(round to the fourth
decimal place).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb6a9708-e09f-4828-b8c7-39fbe4407ad9%2Feaf21460-3d6f-46b3-8b7c-5538ea76bd48%2Fxdfthf_processed.png&w=3840&q=75)
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