The Numerical Unified Transform Method for Initial-boundary Value Problems on the Half-line

2020/06/10 by Bernard Deconinck, Deconinck, Bernard, Thomas Trogdon +3
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2006.06024

openalex publication_date 2020/06/10 · openalex created_date 2020/06/19 · openalex updated_date 2026/07/28

Abstract

We implement the Unified Transform Method of Fokas as a numerical method to solve linear partial differential equations on the half-line. The method computes the solution at any x and t without spatial discretization or time stepping. With the help of contour deformations and oscillatory integration techniques, the method's complexity does not increase for large x,t and the method is more accurate as x,t increase. Our goal is to make no assumptions on the functional form of the initial or boundary functions while maintaining high accuracy in a large region of the (x,t) plane.

Citations

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