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RK4 in Haskell
Ran across this today. It’s a well written implementation of RK4. 4th order Runge-Kutta (RK4) integration in Haskell
Posted in Mathematics, Programming
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Line Segment to Circle Collision/Intersection Detection
Style and Notation All variables are represented in italics except in the diagrams and Python code. Vectors are shown in bold except in the diagrams and Python code. The notation |a| is used to represent the length of a vector … Continue reading
Posted in Computational Geometry, Mathematics, Physics, Programming
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Improved RK4 Implementation
This is a Python implementation of the RK4 numerical integrator that works with differential functions of all orders. That is, any function in the form F(x, y, y’, y”, …, ). If you’re new to numerical integration or even RK4 … Continue reading
Posted in Mathematics, Physics, Programming
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Extending derivatives and integrals into fractions
In the previous post, I wrote about a way to generalize derivatives and integrals into one function. What happens if a number other than an integer is passed to that function? Here is the generalization from the last post: Set … Continue reading
Posted in Mathematics
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Generalizing derivatives and integrals
Start with a simple expression, , and take a few derivatives: A pattern is emerging: , where c is the coefficient. Now the hard part is finding the pattern in the coefficient. This needs to be taken out of the … Continue reading
Posted in Mathematics
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Fourth order Runge-Kutta numerical integration
Here’s a Python implementation of RK4, hardcoded for double-integrating the second derivative (acceleration up to position). For a more generalized solution, see my other implementation. I tried to keep this as simple as I could, so people can easily see … Continue reading
Posted in Mathematics, Physics, Programming
6 Comments