B15. Given the data k 0. 1 3 Ik -1 0. 2 f(Tk) 1.54 2 1.54 0.58 (a) Find an interpolation polynomial of degree three matching the following points. 2.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Please Solve B15a
ku,
for
Suo. <1
%3D
subject to u(0, z) 3D
and
on (0, x) 0.
10.
B14. (a) Use a three point scheme and stepsize of h = 0.01 to estimate the derivativ
r'Inr 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
k
0.
2
3
Ik
-1
0.
2
f(rk) 1.54 2
1.54 0.58
(a) Find an interpolation polynomial of degree three matching the following
points.
(b) Use any three points to fit a natural cubic spline to the date.
B16. Given the following system of equations,
2.x1+3r2 +2r3 = 5
2.x1+2x2 +3x3
12
%3D
ri+3.r2+3.r3 = 5
Solve the system using
(a) the LU decomposition.
(b) an iteration, starting with initial solution x" 4.-3, 4, and performing
iterations.
Transcribed Image Text:ku, for Suo. <1 %3D subject to u(0, z) 3D and on (0, x) 0. 10. B14. (a) Use a three point scheme and stepsize of h = 0.01 to estimate the derivativ r'Inr 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 k 0. 2 3 Ik -1 0. 2 f(rk) 1.54 2 1.54 0.58 (a) Find an interpolation polynomial of degree three matching the following points. (b) Use any three points to fit a natural cubic spline to the date. B16. Given the following system of equations, 2.x1+3r2 +2r3 = 5 2.x1+2x2 +3x3 12 %3D ri+3.r2+3.r3 = 5 Solve the system using (a) the LU decomposition. (b) an iteration, starting with initial solution x" 4.-3, 4, and performing iterations.
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