Numerical Solution of Ordinary Differential Equations 9-5
In the third step
∴
1.03920.04
0.0185
1.03920.04
1.03920.01851.0577at 0.06
yx
yx
−
Δ=Δ=
+
=+==
In the fourth step
∴
1.05770.06
0.0179
1.05770.06
1.05770.01791.0756at 0.08
yx
yx
−
Δ=Δ=
+
=+==
In the fifth step
∴
1.07560.08
0.0172
1.07560.08
1.07560.01721.0928at 0.10
yx
yx
−
Δ=Δ=
+
=+==
9.2.4 Method 4: Euler’s Modified
Method or Heun’s Method
In this method first we convert the differential equa-
tion of the IVP
y′(x) = f (x, y(x)), y(x
0
) = y
0
(9.17)
into an integral equation by integrating both sides
of (9.17)
==−
′
∫∫
11
00
10
(,())()()()
xx
xx
fxyxdxyxdxyxyx
(9.18)
where the antideriv
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month, and much more.