a) Solve the following initial value problem, y'e 2 2y, y(0) = 0.1, 0≤x≤1, for x = 0(0.5)1 by using third order Taylor's series method. b) Solve the following initial value problem, = y' = 2xy², y(0) = 1, 0≤x≤1, 0(0.5)1 by using fourth order Runge-Kutta method.
a) Solve the following initial value problem, y'e 2 2y, y(0) = 0.1, 0≤x≤1, for x = 0(0.5)1 by using third order Taylor's series method. b) Solve the following initial value problem, = y' = 2xy², y(0) = 1, 0≤x≤1, 0(0.5)1 by using fourth order Runge-Kutta method.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![a) Solve the following initial value problem,
for x =
y' = e 2 - 2y, y(0) = 0.1, 0≤x≤1,
0(0.5)1 by using third order Taylor's series method.
b) Solve the following initial value problem,
y = 2xy², y(0) = 1, 0≤x≤1,
for x = 0(0.5)1 by using fourth order Runge-Kutta method.
c) Solve the boundary value problem given as
y' Y
with boundary conditions
y" +
x
=
=
1,
y' (0.5) -0.0283, y(4.5) = 2,
for x = 0.5(1)4.5 by using finite difference method.
[Hint: Do not solve the system Ay = b.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa326aca-745f-410c-a63e-6ad225fdb3f7%2F9a646e24-8522-4d02-825c-3e8368640d3c%2Fr26qeq7_processed.png&w=3840&q=75)
Transcribed Image Text:a) Solve the following initial value problem,
for x =
y' = e 2 - 2y, y(0) = 0.1, 0≤x≤1,
0(0.5)1 by using third order Taylor's series method.
b) Solve the following initial value problem,
y = 2xy², y(0) = 1, 0≤x≤1,
for x = 0(0.5)1 by using fourth order Runge-Kutta method.
c) Solve the boundary value problem given as
y' Y
with boundary conditions
y" +
x
=
=
1,
y' (0.5) -0.0283, y(4.5) = 2,
for x = 0.5(1)4.5 by using finite difference method.
[Hint: Do not solve the system Ay = b.]
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