Symmetry Methods for Discrete Equations and Their Applications

• Project/Area Number: 24K06852
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Keio University
• Principal Investigator: 彭 林玉 慶應義塾大学, 理工学部(矢上), 准教授 (90725780)
• Project Period (FY): 2024-04-01 – 2028-03-31
• Project Status: Granted (Fiscal Year 2024)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2027: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2026: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2025: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2024: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: Symmetry / Conservation law / Lie group / Discrete equations / Numerical methods

Outline of Research at the Start

Symmetries have proven to be of great importance in various fields, owing to the versatile applications in elucidating solution properties to physical models. Many scholars made substantial contributions to the study of symmetry methods for discrete equations, giving rise to a plethora of subsequent research and applications. Despite these advancements, a multitude of unresolved questions continued to challenge the field. The primary objective of the current project is to tackle some of the unresolved questions concerning the symmetries of discrete equations and to explore their applications.