Test: Runge Kutta Method - Civil Engineering (CE) MCQ

Range-Kutta method (R-K method):
To solve  with condition y(x₀) = y₀
Let 'h' denotes the interval between equidistant values of x, if the initial values are (x₀ , y₀), then the first increment in y is computed from the formula given by:
y₁ = y₀ + Δy
where Δy is the change in y given by

y₀ is the intial value of y
y₁ is the changed value of y
Calculation:
Given:



y₁ = y₀ + Δy
y₁ = 1 + 0.1959 = 1.1959

As we can see from the above table, the method used for solving an ordinary differential equation is the Runge Kutta method, and the above-given equation, i.e,    for gradually varied flow profile is an ordinary differential equation. 
So, the Runge Kutta method can be used for finding the solution to the above equation.

Working rule to find increment k of y corresponding to an increment h of x by Runge-Kutta method from  is as follows:

Calculation:
Given:
 y(0) = 2 and step-size (h) = 0.1
Ranga-Kutta fourth order equation is given by:
y₁=y₀+k
where k = 1/6(k₁+2k₂+2k₃+k4) and