Numerical scheme based on the spectral method for calculating nonlinear hyperbolic evolution equations
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High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with the order of total calculation cost O(N log 2N) is proposed. As benchmark results, the relation between the numerical precision and the discretization unit size are demonstrated.
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