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Legendre spectral collocation method for second-order nonlinear ordinary/partial differential equations

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  • We propose an efficient Legendre-Gauss collocation algorithm for second-order nonlinear ordinary differential equations (ODEs). We also design a Legendre-Gauss-type collocation algorithm for time-dependent second-order nonlinear partial differential equations (PDEs), which can be implemented in a synchronous parallel fashion. Numerical results indicate the high accuracy and effectiveness of the suggested algorithms.
    Mathematics Subject Classification: Primary: 65M70, 41A10, 65L05, 35L20.


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