In this paper, we review some results on the spectral methods. We first consider the Jacobi
spectral method and the generalized Jacobi spectral method for various problems, including …

A fully diagonalized spectral method using generalized Laguerre functions is proposed and
analyzed for solving elliptic equations on the half line. We first define the generalized …

In this paper, we develop a general theory of quasi-orthogonal polynomials. We first derive
three-term recurrence relation and second-order differential equations for quasi-orthogonal …

In this paper, we investigate spectral element method for fourth order problems with mixed
inhomogeneous boundary conditions. Some results on the composite Legendre quasi …

In this paper, we propose a collocation method for an initial-boundary value problem of the
generalized nonlinear Klein-Gordon equation. It possesses the spectral accuracy in both …

In this paper, we propose efficient space-time spectral methods for problems on unbounded
domains. For this purpose, we first introduce two series of new basis functions on the …

In this paper, we propose a Fourier-Laguerre spectral method for exterior problems of two-
dimensional complex obstacles based on the mapping method. We first use a polar …

In this paper, we propose a new Galerkin spectral element method for one-dimensional
fourth-order boundary value problems. We first introduce some quasi-orthogonal …

In this paper, we develop domain decomposition spectral method for mixed inhomogeneous
boundary value problems of high order differential equations defined on unbounded …

In this work, we study a new spectral Petrov-Galerkin approximation of space-time fractional
reaction-diffusion equations with viscosity terms built by Riemann-Liouville fractional-order …