Use Runge-Kutta method of order 2 to solve y′ = xy, y(1) = 1, in [1, 1.4] by taking step-length h = 0.2
Runge - Kutta method of order 2
We begin with two functions evaluates of the form:
The and are unknown quantities. The idea was to take a linear combination of the
terms to obtain an approximation for the y value at and to find appropriate values of and .
By comparing the values obtains using Taylor's Series method and the above terms (I will spare you the details here), they obtained the following, which is Runge-Kutta Method of Order 2:
We have: y(1) = 1 [1, 1.4] h = 0.2
We start with x = 0 and y = 1. We'll find the F values first.
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