why we go for RK Method, instead of Euler's Method, Even it also contains the visual explanation of RK Method, Easy to Understand with visual pictures fully Explained.

2. WHY RK METHOD ?
• The Runge-Kutta Method is a numerical integration technique
which provides a better approximation to the equation of
motion. Unlike the Euler's Method, which calculates one slope
at an interval, the Runge-Kutta calculates four different slopes
and uses them as weighted averages.

3. • 1) At time interval t0, calculate slope k1.
• 2) Create a triangle by projecting k1 to t+∆t.

4. • 3) Calculate half the height of the triangle, (∆t/2) k1, and draw a
horizontal line.
• 4) Draw a vertical line at interval t+(1/2)∆t.
• 5) At this intersection point, calculate the slope k2.

5. • 6) Starting out with k2, create a triangle by projecting k2 to
t+(3/2)∆t.
• 7) Calculate half the height of the triangle, (∆t/2)k2.

6. • 8) Translate the height to the base of the triangle formed by k1
at t+(1/2)∆t.

7. • 10) Create the another triangle by projecting k3 to t+(3/2)∆t
• 11) Find half the height of the triangle, (∆t/2)k3

8. • 13) Find the slope k4.

9. THE RUNGA-KUTTA USES THESE SLOPES AS WEIGHTED AVERAGE TO
BETTER APPROXIMATE THE ACTUAL SLOPE, VELOCITY, OF THE
OBJECT. THE POSITION OF THE OBJECT IS THEN CALCULATED USING
THIS NEW SLOPE.

10. • I hope this visual depiction of the Runge-Kutta method helps.