Multidomain pseudospectral approximations to nonlinear convection-diffusion equations are considered. The schemes are formulated with the Legendre-Galerkin method but the nonlinear term is collocated at the Legendre/Chebyshev-Gauss-Lobatto points inside each subinterval. Appropriate base functions are introduced so that the matrix of the system is sparse, and the method can be implemented efficiently and in parallel. The stability and the optimal rate of convergence of the methods are proved. Numerical results are given for both the single domain and the multidomain methods to make a comparison.
A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.
In this paper, a numerical method for solving the optimal control （OC） problems is presented. The method is enlightened by the Chebyshev-Legendre （CL） method for solving the partial differential equations （PDEs）. The Legendre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto （CGL） collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.
This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡a （j∈N）, and the processing time of job Jj is bj（j∈N） on a batch processorM. We take makespan （Cmax） as our minimization objective. In this paper, for the problem of FSMP-BI （m identical parallel machines on the first stage and a batch processor on the second stage）, based on the algorithm given by Sung and Choung for the problem of 1 ｜ri, BI｜Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max {O（nlogn）, O（nB）} time. A max {O（nlogn） , O（nB）}time symmetric Algorithm H2 is given then for the problem of BI-FSMP （a batch processor on the first stage and m identical parallel machines on the second stage）.
In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2)-norm is obtained.
