I'm trying to solve two simultaneous differential equations using Runge-Kutta fourth order on Python, the equations are as follows:
d(f(t))/dt=H(f(t),t)
d(g(t))/dt=K(g(t),f(t),(f(t=0))
f & g are two functions depending on time t only.
initial condition of both functions f and g are known.
I need to plot both functions depending on time.
What is the algorithm to do so on Python?
Does the time step affect the result of solving such problem ?
Thank you.
Have you Googled "python Runge-Kutta"? I thkn that you'll find what you need there.
Naturally, the time step does affect the result. It must not be too long. You need to check that your time-step is short enough that it has no influence on the result.
first : Write a method in python to find out value of function for example f(t)
Then, you need to plot the graph between f(t) and t Similar case for g(t) and t ,And these two graph should be on same plot
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Does the time step affect the result of solving such problem ?
Yes... It will, Because the formula depends upon step height
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
you can get more help from :https://www.geeksforgeeks.org/runge-kutta-4th-order-method-solve-differential-equation/
Are you after a solution or want to learn python? As for a solution, try the FortranCalculus (FC) language that got its start by NASA's Apollo Space program.
FC-Compiler™ application is a (free) Calculus-level Compiler that simplifies Tweaking parameters in ones math model. FC solves Algebraic through Ordinary Differential Equations; Laplace transforms; etc. FC is based on Automatic Differentiation that simplifies computer code to an absolute minimum; i.e., a mathematical model, constraints, and the objective (function) definition.
Most math Modeling, Simulations, & Optimizations can be easily solved with a Calculus-level language/compiler. A half-hour per problem should be enough time to code and execute most math problems. Solves Algebraic Equations through Ordinary Differential Equations, for more visit http://fortrancalculus.info/apps/fc-compiler.html . Equations may be implicit, non-linear, Boundary Value Problems (BVP), Initial Value Problems (IVP), etc. Download, install, & execute some demo problems. Simple and its Freeware! (PDE solvers are in the works!)
For more, see https://www.researchgate.net/post/Solve_YOUR_ODEs_how_to
- Badges
- Science topic
- Similar topics
- Computer Science and Engineering
- Programming Languages
- Python