Consider an ordinary differential equation dw = 0

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Consider an ordinary differential equation dw = 0 - iz
dz

If x = x₀ at t = 0 , the increment in x calculated using Runge-Kutta fourth order multi-step method with a step size of ∆t = 0.2 is

1. 0.22
2. 0.44
3. 0.66
4. 0.88

Correct Option: D

Given ,	dx	= 4t + 4
	dt

x = x₀ at t = 0
n = 0.2
Calculate x(0.2) value
K₁ = f(t₀, x₀) = f(0, x 0) = 4

K₂ = f		t₀ +	h	, x₀ +	1	K₁h
			2		2

= f(0 + 0.1, x₀ + 0.4)
= f(0.1, x₀ + 0.4) = 4(0.1) + 4 = 4.4

K₃ = f		x₀ +	h	, x₀ +	1	K₂h
			2		2

= f[t₀ + 0.1, x₀ + (2.2)(0.2)]
= f(0.1, x₀ + 0.44) = 4(0.1) + 4 = 4.4
K₄ = f(t₀ + h, x₀ + K₃ h)
= f(0 + 0.2, x₀ + 0.88)
= f(0.2, x₀ + 0.88)
= 4(0.2) + 4 = 4.8

x(0.2) = x₁ = x₀ +	h	(K₁ + 2K₂ + 2K₃ + K₄)
	6

= x₀ +	0.2	[ 4 + 2(4.4) + 2(4.4) + (4.8) ]
	6

= x₀ +	0.2	(4 + 8.8 + 8.8 + 4.8)
	6

= x₀ + 0.88
Increment as x = x 1 – x₀ = x₀ + 0.88 – x₀ = 0.88