An Integral Equation Method for Linear Two-Point Boundary Value Systems
By: Tianze Zhang, Yixuan Ma, Jun Wang
Potential Business Impact:
Solves hard math problems super fast and accurately.
We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a well-conditioned integral equation. We then make use of a high-order Nystrom discretization and a fast direct solver on the continuous level to obtain a black-box solver that is fast and accurate. A numerical study of the conditioning of different integral formulations is carried out. Excellent performance in speed, accuracy, and robustness is demonstrated with several challenging numerical examples.
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