desolver 2.5.9

Differential Equation System Solver

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

2.5.0 - Event detection has been added to the library. 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

1. Runge-Kutta 45 with Cash-Karp Coefficients
2. Adaptive Heun-Euler Method

Implicit Methods

NOT YET IMPLEMENTED

Fixed Step Methods

Explicit Methods

1. Midpoint Method
2. Heun's Method
3. Euler's Method
4. Euler-Trapezoidal Method
5. BABs9o7H Method -- Based on arXiv:1501.04345v2 - BAB's9o7H
6. ABAs5o6HA Method -- Based on arXiv:1501.04345v2 - ABAs5o6H
7. 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)