\(\lambda u\) (lambda_u)

class examples.problems.lambda_u.LambdaU(*args, **kwargs)

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

\(u'(t, \phi_t) = \lambda u(t, \phi_t)\)

Describes the following first-order ODE initial value problem:

\[\begin{split}\begin{align} u'(t, \phi_t) &= \lambda u(t, \phi_t) \\ u(t, 0) &= 1 \end{align}\end{split}\]

With the exact solution:

\[u(t, \phi_t) = e^{\lambda\phi_t}\]

Parameters:lmbda (float) – (optional) Coefficient \(\lambda\)

direct_implicit(*args, **kwargs)

Direct Implicit Formula for \(u'(t, \phi_t) &= \lambda u(t, \phi_t)\)