Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.cnsns.2020.105510 Hassan Khosravian-Arab , M. R. Eslahchi
This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-Müntz functions presented by the authors recently. These basis functions are, in fact, generalized forms of the newly generated Jacobi based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail. The pseudo-spectral differentiation (and integration) matrices have been extracted in two different manners. Some numerical experiments are provided to show the efficiency and capability of these newly generated non-classical Lagrange basis functions.
中文翻译:
Müntz伪谱方法:理论和数值实验
本文介绍了两个新的非经典Lagrange基函数,它们基于作者最近提出的新Jacobi-Müntz函数。这些基本函数实际上是新生成的基于Jacobi的函数的广义形式。针对这些非经典Lagrange基函数,介绍了两个非经典插值,并详细证明了它们的误差范围。伪光谱微分(和积分)矩阵已经以两种不同的方式提取。提供了一些数值实验来显示这些新生成的非经典Lagrange基函数的效率和功能。