Jacobi orthogonal approximation with negative integer and its application to ordinary differential equations

Advances in Difference Equations

Zheng-su Wan¹  Xiao-yong Zhang² 

[1] Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, China;Department of Mathematics, Shanghai Maritime University, Shanghai, China

关键词: Jacobi approximation with negative integer;    spectral method;    ordinary differential equation;    35Q99;    35R35;    65M12;    65M70;   

DOI  :  10.1186/s13662-015-0562-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the Jacobi spectral method for ordinary differential equations, which is based on the Jacobi approximation with negative integer, is proposed. This method is very efficient for the initial value problem of ordinary differential equations. The global convergence of proposed algorithm is proved. Numerical results demonstrate the spectral accuracy of this new approach and coincide well with theoretical analysis.

【 授权许可】

CC BY