(b) The Runge-Kutta method of order 2 (RK2) with h = 0.1 is used to solve dy y + ry dr with y(0) = 1 in order to find y(0.3) correct to four decimal places. Assuming that the local error in RK2 is given by "(E), E E [r, "141], 6 estimate an upper bound for the global error at a 0.3.

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
5 b
(a) Given the initial value problem
dy
x + y + sin (x + y) + cos (ry) +
= 0, y (0) = 0,
dz
approximate y (1), with h = 0.1.
%3D
(b) The Runge-Kutta method of order 2 (RK2) with h = 0.1 is used to solve
dy
-y + xy
dx
with y(0) = 1 in order to find y(0.3) correct to four decimal places. Assuming
that the local error in RK2 is given by
h3
y"(E), E E [2, r 141],
€i+1
estimate an upper bound for the global error at a = 0.3.
Transcribed Image Text:(a) Given the initial value problem dy x + y + sin (x + y) + cos (ry) + = 0, y (0) = 0, dz approximate y (1), with h = 0.1. %3D (b) The Runge-Kutta method of order 2 (RK2) with h = 0.1 is used to solve dy -y + xy dx with y(0) = 1 in order to find y(0.3) correct to four decimal places. Assuming that the local error in RK2 is given by h3 y"(E), E E [2, r 141], €i+1 estimate an upper bound for the global error at a = 0.3.
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