A nonlinear optimization approach to the construction of general linear methods of high order

[摘要] We describe the construction of diagonally implicit multistage integration methods of order and stage order p = q = 7 and p = q = 8 for ordinary differential equations. These methods were obtained using state-of-the-art optimization methods, particularly variable-model trust-region least-squares algorithms.

[发布日期] 1997-07-08

[关键词] general linear method;ordinary differential equation;A-stability;L-stability;least-squares minimization