Error estimation of Hermite spectral method for nonlinear partial differential equations
Mathematics of Computation
Combined Hermite spectral-finite difference method for the Fokker-Planck equation
Mathematics of Computation
Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains
SIAM Journal on Numerical Analysis
Generalized Jacobi Rational Spectral Method and Its Applications
Journal of Scientific Computing
Generalized Hermite Spectral Method and its Applications to Problems in Unbounded Domains
SIAM Journal on Numerical Analysis
Generalized Jacobi rational spectral method on the half line
Advances in Computational Mathematics
Journal of Computational and Applied Mathematics
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In this paper, we propose the generalized Hermite spectral method by using a family of new generalized Hermite functions, which are mutually orthogonal with the weight function (1+x^2)^-^@c, @c being an arbitrary real number. We establish the basic results on the corresponding orthogonal approximation and interpolation, which simulate the asymptotic behaviors of approximated functions at infinity reasonably. As examples of applications, the spectral schemes are provided for two model problems. Numerical results demonstrate their spectral accuracy in space.