. Given the following system of equations, 2x1 +3r2+2r3 = 5 %3D 2.r1 +2r2 +3r3 = 12 %3D Ii+3r2 +3r3 = 5 %3D Solve the system using (a) the LU decomposition.

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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Solve B16a
(b) Find the bounded solution of
Pu
- ku,
for -oc < <o, t>0
subject to u(0, z):
Ug, r< 1
du
and
(0, z) 0.
%3D
10, 1피> 0
at
B14. (a) Use a three point scheme and stepsize of h = 0.01 to estimate the derivative
3 In r at r = 2.
(b) Consider the initial value problem
dy
+y = yt/(t +y),
y(-1) = 2.
dt
Estimate y(0.2) using the Runge-Kutta method with stepsize 0.1.
B15. Given the data
0.
3.
Ik
-1
0.
f(rk) 1.54 2 1.54 0.58
(a) Find an interpolation polynomial of degree three matching the following fo
points.
(b) Use any three points to fit a natural cubic spline to the date.
B16. Given the following system of equations,
2x1 +3r2+2r3 =
2.r1 +2x2+3r3
12
%3D
ri+3r2 +3r3 =
Solve the system using
(a) the LU decomposition.
(b) an iteration, starting with initial solution x° = (4.-3. 4", and performing fo
iterations.
page
Transcribed Image Text:(b) Find the bounded solution of Pu - ku, for -oc < <o, t>0 subject to u(0, z): Ug, r< 1 du and (0, z) 0. %3D 10, 1피> 0 at B14. (a) Use a three point scheme and stepsize of h = 0.01 to estimate the derivative 3 In r at r = 2. (b) Consider the initial value problem dy +y = yt/(t +y), y(-1) = 2. dt Estimate y(0.2) using the Runge-Kutta method with stepsize 0.1. B15. Given the data 0. 3. Ik -1 0. f(rk) 1.54 2 1.54 0.58 (a) Find an interpolation polynomial of degree three matching the following fo points. (b) Use any three points to fit a natural cubic spline to the date. B16. Given the following system of equations, 2x1 +3r2+2r3 = 2.r1 +2x2+3r3 12 %3D ri+3r2 +3r3 = Solve the system using (a) the LU decomposition. (b) an iteration, starting with initial solution x° = (4.-3. 4", and performing fo iterations. page
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