Time Complexity Analysis of Quantum Difference Methods for Multiscale Transport Equations

DOI10.4208/eajam.2022-315.200423OpenAlexW4378009077MaRDI QIDQ6069454

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Publication date: 16 December 2023

Published in: East Asian Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/eajam.2022-315.200423

zbMATH Keywords

time complexityasymptotic-preserving schemesquantum difference methodsmultiscale transport equations

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Applications of Lie groups to the sciences; explicit representations (22E70) Perturbation theories for operators and differential equations in quantum theory (81Q15) Time series analysis of dynamical systems (37M10) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Transport equations (35Q49)

Cites Work

• Transport equations for elastic and other waves in random media
• Quantum algorithm for linear differential equations with exponentially improved dependence on precision
• Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations
• Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
• Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
• Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Hamiltonian simulation with nearly optimal dependence on spectral norm
• High-order quantum algorithm for solving linear differential equations
• Asymptotic-preserving schemes for multiscale physical problems
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