Differential Equation System Solver
Project description
DESolver
This is a python package for solving Initial Value Problems using various numerical integrators. Many integration routines are included ranging from fixed step to symplectic to adaptive integrators.
Implicit integrators are intended for release 3.0, but that's far off for now.
Latest Release
2.2.0 - PyTorch backend is now implemented. It is now possible to numerically integrate a system of equations that use pytorch tensors and then compute gradients from these. Requires installation of PyTorch from here. Torch backend will not work without pytorch!
To Install:
Just type
pip install desolver
Implemented Integration Methods
Adaptive Methods
Explicit Methods
- Runge-Kutta 45 with Cash-Karp Coefficients
- Adaptive Heun-Euler Method
Implicit Methods
NOT YET IMPLEMENTED
Fixed Step Methods
Explicit Methods
- Midpoint Method
- Heun's Method
- Euler's Method
- Euler-Trapezoidal Method
- BABs9o7H Method -- Based on arXiv:1501.04345v2 - BAB's9o7H
- ABAs5o6HA Method -- Based on arXiv:1501.04345v2 - ABAs5o6H
- Runge-Kutta 5 - The 5th order integrator from RK45. Very accurate with fixed step size.
Implicit Methods
NOT YET IMPLEMENTED
Minimal Working Example
This example shows the integration of a harmonic oscillator using DESolver.
import desolver as de
import desolver.backend as D
@de.rhs_prettifier("""[vx, x]""")
def rhs(t, state, **kwargs):
x,vx = state
dx = vx
dvx = -x
return D.array([dx, dvx])
y_init = D.array([1., 0.])
a = de.OdeSystem(rhs, y0=y_init, dense_output=True, t=(0, 2*D.pi), dt=0.01, rtol=1e-6, atol=1e-9)
a.show_system()
a.integrate()
print(a)
print("If the integration was successful and correct, a[0].y and a[-1].y should be near identical.")
print(a[0].y, a[-1].y)
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