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<p>We propose a high-order numerical scheme for time-dependent first-order Hamilton-Jacobi-Bellman (HJB) equations. In particular, we propose to combine a semi-Lagrangian (SL) scheme with a Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction. The CWENO method provides a non-oscillatory, high-order reconstruction polynomial that allows efficient evaluations at multiple reconstruction points, while the SL method ensures stability without any time-step restrictions. Together, they form a particularly effective framework for solving HJB equations. We prove a convergence result in the case of state- and time-independent Hamiltonians. Numerical simulations are presented in space dimensions one and two, also for more general state- and time-dependent Hamiltonians, demonstrating superior performance in terms of CPU time gain compared with a semi-Lagrangian scheme coupled with Weighted Non-Oscillatory reconstructions.</p>

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A CWENO Large Time-Step Scheme for Hamilton-Jacobi Equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月9日

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  • Elisabetta Carlini,
  • Roberto Ferretti,
  • Silvia Preda,
  • Matteo Semplice

摘要

We propose a high-order numerical scheme for time-dependent first-order Hamilton-Jacobi-Bellman (HJB) equations. In particular, we propose to combine a semi-Lagrangian (SL) scheme with a Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction. The CWENO method provides a non-oscillatory, high-order reconstruction polynomial that allows efficient evaluations at multiple reconstruction points, while the SL method ensures stability without any time-step restrictions. Together, they form a particularly effective framework for solving HJB equations. We prove a convergence result in the case of state- and time-independent Hamiltonians. Numerical simulations are presented in space dimensions one and two, also for more general state- and time-dependent Hamiltonians, demonstrating superior performance in terms of CPU time gain compared with a semi-Lagrangian scheme coupled with Weighted Non-Oscillatory reconstructions.