A family of matrix coefficient formulas for solving ordinary differential equations

作者：

Highlights：

• A new family of numerical methods is proposed for solving ODEs.

• Its coefficients can be in a matrix form.

• It can have A-stability and explicit formulation.

• It can be explicitly or implicitly implemented.

• It is of high computational efficiency for solving stiff problems in contrast to conventional implicit methods.

摘要

•A new family of numerical methods is proposed for solving ODEs.•Its coefficients can be in a matrix form.•It can have A-stability and explicit formulation.•It can be explicitly or implicitly implemented.•It is of high computational efficiency for solving stiff problems in contrast to conventional implicit methods.

论文关键词：Eigen-dependent formula,Problem-dependent formula,Eigen-decomposition,Eigenvalue,Eigenmode,Accuracy,Stability

论文评审过程：Received 22 April 2021, Revised 7 July 2021, Accepted 15 November 2021, Available online 9 December 2021, Version of Record 9 December 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126811