8. Problem 1
Given
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦, with initial conditions 𝑦 0 = 1. Choose ℎ = 0.
𝑦 0.1 , 𝑦 0.2 and 𝑦 0.3 using Runge-Kutta’s method of fourth o
9. Problem 1
Given
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦, with initial conditions 𝑦 0 = 1. Choose ℎ = 0.
𝑦 0.1 , 𝑦 0.2 and 𝑦 0.3 using Runge-Kutta’s method of fourth o
Putting 𝑛 = 0 in Runge-Kutta’s formula for fourth order, we get
10. Problem 1
Given
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦, with initial conditions 𝑦 0 = 1. Choose ℎ = 0.
𝑦 0.1 , 𝑦 0.2 and 𝑦 0.3 using Runge-Kutta’s method of fourth o
Putting 𝑛 = 0 in Runge-Kutta’s formula for fourth order, we get
𝑦1 = 𝑦0 +
1
6
𝑘1 + 2𝑘2 + 2𝑘3 + 𝑘4
11. Problem 1
Given
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦, with initial conditions 𝑦 0 = 1. Choose ℎ = 0.
𝑦 0.1 , 𝑦 0.2 and 𝑦 0.3 using Runge-Kutta’s method of fourth o
Putting 𝑛 = 0 in Runge-Kutta’s formula for fourth order, we get
𝑦1 = 𝑦0 +
1
6
𝑘1 + 2𝑘2 + 2𝑘3 + 𝑘4
where 𝑘1 = ℎ𝑓 𝑥0, 𝑦0 = 0.1 0 + 1 = 0.1
12. Problem 1
Given
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦, with initial conditions 𝑦 0 = 1. Choose ℎ = 0.
𝑦 0.1 , 𝑦 0.2 and 𝑦 0.3 using Runge-Kutta’s method of fourth o
Putting 𝑛 = 0 in Runge-Kutta’s formula for fourth order, we get
𝑦1 = 𝑦0 +
1
6
𝑘1 + 2𝑘2 + 2𝑘3 + 𝑘4
where 𝑘1 = ℎ𝑓 𝑥0, 𝑦0 = 0.1 0 + 1 = 0.1
𝑘2 = ℎ𝑓 𝑥0 +
ℎ
2
, 𝑦0 +
𝑘1
2
= 0.1 0.05 + 1.05
13. Problem 1
Given
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦, with initial conditions 𝑦 0 = 1. Choose ℎ = 0.
𝑦 0.1 , 𝑦 0.2 and 𝑦 0.3 using Runge-Kutta’s method of fourth o
Putting 𝑛 = 0 in Runge-Kutta’s formula for fourth order, we get
𝑦1 = 𝑦0 +
1
6
𝑘1 + 2𝑘2 + 2𝑘3 + 𝑘4
where 𝑘1 = ℎ𝑓 𝑥0, 𝑦0 = 0.1 0 + 1 = 0.1
𝑘2 = ℎ𝑓 𝑥0 +
ℎ
2
, 𝑦0 +
𝑘1
2
= 0.1 0.05 + 1.05
𝑘3 = ℎ𝑓 𝑥0 +
ℎ
2
, 𝑦0 +
𝑘2
2
= 0.1 0.05 + 1.05
14. Problem 1
Given
𝑑𝑦
𝑑𝑥
= 𝑥 + 𝑦, with initial conditions 𝑦 0 = 1. Choose ℎ = 0.
𝑦 0.1 , 𝑦 0.2 and 𝑦 0.3 using Runge-Kutta’s method of fourth o
Putting 𝑛 = 0 in Runge-Kutta’s formula for fourth order, we get
𝑦1 = 𝑦0 +
1
6
𝑘1 + 2𝑘2 + 2𝑘3 + 𝑘4
where 𝑘1 = ℎ𝑓 𝑥0, 𝑦0 = 0.1 0 + 1 = 0.1
𝑘2 = ℎ𝑓 𝑥0 +
ℎ
2
, 𝑦0 +
𝑘1
2
= 0.1 0.05 + 1.05
𝑘3 = ℎ𝑓 𝑥0 +
ℎ
2
, 𝑦0 +
𝑘2
2
= 0.1 0.05 + 1.05
𝑘4 = ℎ𝑓 𝑥0 + ℎ, 𝑦0 + 𝑘3 = 0.1 0.1 + 1.110