In this survey,we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems.These methods offer a valuable synthesis between classical Runge-Kutta met...In this survey,we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems.These methods offer a valuable synthesis between classical Runge-Kutta methods,introduced more than a century ago,and exponential integrators,which date back to the 1960s.This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience.展开更多
基金support of Gruppo Nazionale per il Calcolo Scientifico of Istituto Nazionale di Alta Matematica.Her work was partially supported by the Italian Ministry of University and Research through the PRIN 2022 project(No.20229P2HEA)“Stochastic numerical modelling for sustainable innovation”,Unit of Udine(CUP G53C24000710006)support of Gruppo Nazionale per l’Analisi Matematica,la Probabilitàe le loro Applicazioni of Istituto Nazionale di Alta Matematica and moreover acknowledges the support of the MIUR-PRIN 2022 project“Nonlinear dispersive equations in presence of singularities”(No.20225ATSTP)support of Gruppo Nazionale di Fisica Matematica of Istituto Nazionale di Alta Matematica.
摘要In this survey,we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems.These methods offer a valuable synthesis between classical Runge-Kutta methods,introduced more than a century ago,and exponential integrators,which date back to the 1960s.This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience.