多维区域中非线性偏微分方程的修正Laguerre谱与拟谱方法

研究多维区域中非线性偏微分方程的谱与拟谱方法．建立了修正Laguerre正交逼近与插值结果，这些结果对于建立和分析无界区域中的数值方法起着重要的作用．作为结果的一个应用，研究了二维无界区域中的Logistic方程的修正Laguerre谱格式,证明了它的稳定性和收敛性．数值试验结果表明所提出方法具有很高的精度，与理论分析结果完全吻合．

Modified Laguerre Spectral and Pseudospectral Methods for Nonlinear Partial Differential Equations in Multiple Dimensions

The Laguerre spectral and pseudospectral methods for multiple-dimensional nonlinear pardifferential equations are investigated. Some results on the modified Laguerre orthogonal approximation and interpolation were established, which play important roles in the related numerical methods for unbounded domains. As an example, the modified LAguerre spectral and pseudospectal methods were proposed for two-dimensional Logistic equation. The stability and convergence of suggested schemes were proved. Numerical results demonstrate the high accuracy of these approaches.