solved for this question 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 atI = 0, x = 1 and z = 2: y (0) =, y(1) =y(2) =Round the answerto the fourth decimal place (Hint: You may proceed as in Q2 and Q3 of tutorial 7. Also note that by default, Matlab rounds the answerto 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. Useh = 0.1to determine the solution at a(Round the answer to the fourth decimal place). • The initial value problem y/ =cos (ry), y(1) = 2 is to be solved on the interval z E [1,3] using the forward Eulermethod 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).drdt• The initial value problem, z(0) = 1, y(0) = –-lis to be solved on the interval t e [0, 1] using the3In+1backward 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 IYn +1is 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 att = 1: #(1) =(round to the fourth decimal place) and y(1)|(round to the fourthdecimal place).

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Description: solved for this question 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

The boundary value problem is y''(x)-x2y(x)=0 The given condition is y(3)=2, y'(0)=1 The solution of…

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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).

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).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

solved for this question

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).

• 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).

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