A Stiff MOL Boundary Control Problem for the 1D Heat Equation with Exact Discrete Solution

@article{Lang2022ASM,
  title={A Stiff MOL Boundary Control Problem for the 1D Heat Equation with Exact Discrete Solution},
  author={Jens Lang and Bernhard A. Schmitt},
  journal={ArXiv},
  year={2022},
  volume={abs/2209.14051}
}
Method-of-lines discretizations are demanding test problems for stiff integration methods. However, for PDE problems with known analytic solution the presence of space discretization errors or the need to use codes to compute reference solutions may limit the validity of numerical test results. To over-come these drawbacks we present in this short note a simple test problem with boundary control, a situation where one-step methods may suffer from order reduction. We derive exact formulas for the… 

Figures from this paper

References

SHOWING 1-9 OF 9 REFERENCES

Runge-Kutta methods for partial differential equations and fractional orders of convergence

. We apply Runge-Kutta methods to linear partial differential equations of the form u¡(x, t) =5?(x, d)u(x, t)+f(x, t). Under appropriate assumptions on the eigenvalues of the operator 5C and the

Runge-Kutta approximation of quasi-linear parabolic equations

It is shown that the convergence properties of implicit Runge-Kutta meth- ods applied to time discretization of parabolic equations with time- or solution- dependent operator depends on the type of boundary conditions.

Discrete Adjoint Implicit Peer Methods in Optimal Control

Symplectic Runge-Kutta Schemes for Adjoint Equations, Automatic Differentiation, Optimal Control, and More

The symp eclecticness (or lack of symplecticness) of a Runge--Kutta or partitioned Runge-kutta integrator should be relevant to understanding its performance when applied to the computation of sensitivities, to optimal control problems, and in othe...

Runge-Kutta methods in optimal control and the transformed adjoint system

  • W. Hager
  • Computer Science
    Numerische Mathematik
  • 2000
The analysis utilizes a connection between the Kuhn-Tucker multipliers for the discrete problem and the adjoint variables associated with the continuous minimum principle to determine the convergence rate for Runge-Kutta discretizations of nonlinear control problems.

Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems

This paper is concerned with the construction and convergence analysis of novel implicit Peer triplets of two-step nature with four stages for nonlinear ODE constrained optimal control problems. We

Practical Methods for Optimal Control and Estimation Using Nonlinear Programming

Variational Calculus and Optimal Control