Constant (constant)

class examples.problems.constant.Constant(constant=-1.0, shift=1.0, *args, **kwargs)

Bases: pypint.problems.i_initial_value_problem.IInitialValueProblem, pypint.problems.has_exact_solution_mixin.HasExactSolutionMixin

\(u'(t, \phi_t) &= C\)

Describes the following first-order ODE initial value problem:

\[\begin{split}\begin{align} u'(t, \phi_t) &= C \\ u(t, 0) &= IV \end{align}\end{split}\]

With the exact solution:

\[u(t, \phi_t) = 1-IV\phi_t\]

Parameters:

• constant (float) – Constant value \(C\)
• shift (float) – Initial value \(IV\), which is the shift along the \(y\) axis.