ON THE EXPLICIT TWO-STAGE FOURTH-ORDER ACCURATE TIME DISCRETIZATIONS  

作　　者：Yuhuan Yuan Huazhong Tang 

机构地区：[1]Center for Applied Physics and Technology,HEDPS and LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China [2]Nanchang Hangkong University,Nanchang 330063,China

出　　处：《Journal of Computational Mathematics》2023年第2期305-324,共20页计算数学（英文）

基　　金：partially supported by the Special Project on Highperformance Computing under the National Key R&D Program(No.2020YFA0712002);the National Natural Science Foundation of China(No.12126302,12171227).

摘　　要：This paper continues to study the explicit two-stage fourth-order accurate time discretizations[5-7].By introducing variable weights,we propose a class of more general explicit one-step two-stage time discretizations,which are different from the existing methods,e.g.the Euler methods,Runge-Kutta methods,and multistage multiderivative methods etc.We study the absolute stability,the stability interval,and the intersection between the imaginary axis and the absolute stability region.Our results show that our two-stage time discretizations can be fourth-order accurate conditionally,the absolute stability region of the proposed methods with some special choices of the variable weights can be larger than that of the classical explicit fourth-or fifth-order Runge-Kutta method,and the interval of absolute stability can be almost twice as much as the latter.Several numerical experiments are carried out to demonstrate the performance and accuracy as well as the stability of our proposed methods.

关 键 词：Multistage multiderivative methods Runge-Kutta methods Absolute stability region Interval of absolute stability 

分 类 号：O175[理学—数学]