The Unified Transform Method for solving partial differential equations

Fokas at Cambridge discovered the unified transform method (UTM) for solving initial-boundary value problems. The method is more general than the traditional classical methods of Fourier and Laplace, and not more complicated to use. We will discuss the method, applying it to a variety of problems, including some that cannot be solved using the classical solution methods. We will start by showing how the method works for problems involving the heat equation, where the classical methods work as well, allowing us to compare. This will give students background in partial differential equations and some complex analysis.

  • References: The Method of Fokas for Solving Linear Partial Differential Equations by Bernard Deconinck, Thomas Trogdon & Vishal Vasan
  • Prerequisites: A course in ordinary differential equations. A course in partial differential equations is not required. Students who have seen partial differential equations will still benefit, as this mentored reading will introduce new material
  • Meeting: Once/week for at least 10 weeks. Depending on progress and student interest, meetings could continue beyond 10 weeks. First meeting would be at the very end of September of the beginning of October.
  • Type: Reading
  • Size: 1-3 Students

Instructor: Bernard Deconinck, Department of Applied Mathematics, University of Washington

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