Well-Posedness of one-way wave equations and absorbing boundary conditions
Mathematics of Computation
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
A comparative study of absorbing boundary conditions
Journal of Computational Physics
Journal of Computational Physics
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SIAM Journal on Scientific Computing
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Diagonally implicit multistage integration methods for pseudospectral solutions of the wave equation
Applied Numerical Mathematics - Auckl numerical ordinary differential equations (ANODE 98 workshop)
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
A note on stability of pseudospectral methods for wave propagation
Journal of Computational and Applied Mathematics
Stability of Gauss–Radau Pseudospectral Approximations of the One-Dimensional Wave Equation
Journal of Scientific Computing
Original article: Lanczos-Chebyshev pseudospectral methods for wave-propagation problems
Mathematics and Computers in Simulation
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In this paper we describe the implementation of one-way wave equations of the second order in conjuction with pseudospectral methods for wave propagation in two space dimensions. These equations are first reformulated as hyperbolic systems of the first order and the absorbing boundaries are implemented by an appropriate modification of the matrix of this system. The resulting matrix corresponding to one-way wave equation based on Padé approximation has all eigenvalues in the complex negative half plane which allows stable integration of the underlying system by any ODE solver in the sense of “eigenvalue stability.” The obtained numerical scheme is much more accurate than the schemes obtained before which utilized absorbing boundary conditions of the first order, and is also capable of integrating the wave propagation problems on much larger time intervals than was previously possible.