JACOBI PSEUDOSPECTRAL METHOD FOR FOURTH ORDER PROBLEMS

In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.     

基于变分原理的三维扩散方程离散化格式

研究三维扩散方程的数值模拟.在非正规六面体网格上,用变分原理建立扩散流形式的差分格式.将扩散流通量作为未知函数,求其泛函极值,并与原函数温度联立求解.详细推导了计算公式,并给出了数值试验结果.     

ON THE L_∞ CONVERGENCE AND THE EXTRAPOLATION METHOD OF A DIFFERENCE SCHEME FOR NONLOCAL PARABOLIC EQUATION WITH NATURAL BOUNDARY CONDITIONS

1. IntroductionNoulocal parabolic equaions have many aPplicatiOns. FOr exaInPle, in COn8W fiuld fiowin a saturated porous mallum, the eqwtion gOvwi the pore presure p(nt) in an odarcylindrical roch sWle is given in [1] astopether withwher c is a material constat with driensiom of velOcity, the COeffilen of conSOlidatbo, ut tyare shear coefficieats and n a material constat, f dentes radial distance and t thae. If t isrePaced by ct and be by q in (1.1), we getVarious ndtial and boundny co…     

解三维扩散方程的积分内插法格式

研究三维扩散方程的数值模拟.在非正规六面体网格上,使用积分内插法建立扩散方程差分格式,涉及到27个相邻网格,适用于大变形网格上带间断系数的拟线性扩散方程的计算.叙述差分格式的建立,推导通量流和网格顶点温度的计算公式,给出了数值试验结果.     

A second order difference scheme with nonuniform rectangular meshes for nonlinear parabolic system

In this paper, a difference scheme with nonuniform meshes is proposed for the initial-boundary problem of the nonlinear parabolic system. It is proved that the difference scheme is second order convergent in both space and time.