Quadrature and solving ODEs (verry.integrate)#

This module provides verified routines for quadrature and solving ordinary differential equations.

Quadrature functions#

cumulative_simpson(fun, a, b, n)

Cumulatively integrate fun using the composite Simpson's 1/3 rule.

cumulative_trapezoid(fun, a, b, n)

Cumulatively integrate fun using the composite trapezoidal rule.

Solving initial value problems for ODEs#

Solvers#

C0Solver([integrator, tracker])

ODE solver.

C1Solver([integrator, tracker, vareq])

ODE solver using variational equations.

Integrators#

Integrator()

Abstract base class for ODE integrators.

IntegratorFactory()

Abstract factory for creating Integrator.

eilo([order, rtol, atol, max_tries, ...])

Factory for creating Integrator based on Eijgenraam and Lohner's algorithm.

kashi([order, rtol, atol, max_tries, ...])

Factory for creating Integrator based on Kashiwagi's algorithm.

Trackers#

Tracker()

Abstract base class for trackers.

TrackerFactory()

Abstract factory for creating Tracker.

affine([n, m])

Factory for creating Tracker using affine arithmetic.

direct()

Factory for creating the most obvious Tracker.

doubleton([tracker])

Factory for creating Tracker using doubleton method.

qr()

Factory for creating Tracker using a QR decomposition.

VarEqSolvers#

VarEqSolver()

Abstract base class for solvers of variational equations.

VarEqSolverFactory()

Abstract factory for creating VarEqSolver.

brute()

Factory for creating VarEqSolver that solves variational equations directly.

lognorm([order])

Factory for creating VarEqSolver that uses a logarithmic norm.

Miscellaneous#

AbortSolving([message])

Raised by a callback function to abort solvers.

C0SolverCallbackArg(t, y, t_prev, series)

Argument of callback functions passed to C0Solver.solve().

C0SolverResultContent(t, y, sol)

Information obtained when C0Solver successfully worked.

C1SolverCallbackArg(t, y, t_prev, series, ...)

Argument of callback functions passed to C1Solver.solve().

C1SolverResultContent(t, y, sol, jac)

Information obtained when C1Solver successfully worked.

ODESolution(ts, series)

Solution of ODEs.

SolverResult(status, content, message)

Output of ODE solvers.

seriessol(fun, t0, y0, deg)

Return the Taylor polynomial of the ODE solution.

variationaleq(fun, sol)

Return the right-hand side of variational equations.