Applied Numerical Mathematics
Applied Numerical Mathematics
Journal of Computational Physics
Numerical approximations to integrals with a highly oscillatory Bessel kernel
Applied Numerical Mathematics
Neumann exterior wave propagation problems: computational aspects of 3D energetic Galerkin BEM
Computational Mechanics
Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval
Journal of Computational and Applied Mathematics
On evaluation of Bessel transforms with oscillatory and algebraic singular integrands
Journal of Computational and Applied Mathematics
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Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations. Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. Here we derive and analyze some new stable collocation schemes for the single layer equation for transient acoustic scattering, and use (spatial) Fourier and (temporal) Laplace transform techniques to demonstrate that such stable schemes are second order convergent.