Legendre Wavelet Collocation Benchmark
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Boundary-Layer-Induced Failure of Standard Physics-Informed Neural Networks: A Legendre Wavelet Collocation Benchmark for Singularly Perturbed Transport Problems
Announce Type: new Abstract: Boundary layers provide a demanding test for numerical solvers because the solution may remain almost constant over most of the domain while changing rapidly in a narrow region near the boundary. This paper studies a singularly perturbed one-dimensional transport boundary-value problem with increasing Peclet number $(\mathrm{Pe})$. A local Legendre wavelet collocation method (LWM) is compared with a standard soft-boundary physics-informed neural network (PINN)...