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 4.0, but that's far off for now.
In Beta Development
3.0.0b12 - PyAudi support has been added to the module. It is now possible to do numerical integrations using gdual variables such as gdual_double, gdual_vdouble and gdual_real128 (only on select platforms, refer to pyaudi docs for more information).
This version can be installed with pip install desolver[pyaudi]==3.0.0b12
Latest Release
2.5.0 - Event detection has been added to the module. It is now possible to do numerical integration with terminal and non-terminal events.
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.
Use of PyTorch backend requires installation of PyTorch from here.
To Install:
Just type
pip install desolver
Implemented Integration Methods
Adaptive Methods
Explicit Methods
- Runge-Kutta 14(12) with Feagin Coefficients [NEW]
- Runge-Kutta 10(8) with Feagin Coefficients [NEW]
- Runge-Kutta 8(7) with Dormand-Prince Coefficients [NEW]
- Runge-Kutta 4(5) with Cash-Karp Coefficients
- Adaptive Heun-Euler Method
Implicit Methods
NOT YET IMPLEMENTED
Fixed Step Methods
Explicit Methods
- Runge-Kutta 4 - The classic RK4 integrator
- Runge-Kutta 5 - The 5th order integrator from RK45 with Cash-Karp Coefficients.
- BABs9o7H Method -- Based on arXiv:1501.04345v2 - BAB's9o7H
- ABAs5o6HA Method -- Based on arXiv:1501.04345v2 - ABAs5o6H
- Midpoint Method
- Heun's Method
- Euler's Method
- Euler-Trapezoidal Method
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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