A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to transform the original problem into a matrix linear ordinary differential equation which is subsequently solved with numerical integrators obtained from the Magnus expansion. The algorithm can be used in the periodic case to get both accurate approximations of the characteristic multipliers and the solution itself. In addition, it can be extended to deal with certain quasilinear delay equations.
An Algorithm for Computing Coefficients of Words in Expressions Involving Exponentials and its Application to the Construction of Exponential Integrators
Trigonometric integrators for quasilinear wave equations
Freie Universität Berlin（柏林自由大学）；Duke University（杜克大学）；UNC-Chapel Hill（北卡罗来纳大学教堂山分校）；Université Paris-Sud（巴黎南大学）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València（瓦伦西亚理工大学多学科数学研究所）；Departament de Matemàtiques and IMAC, Universitat Jaume I（海梅一世大学数学系与IMAC）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）
Magnus-type Integrator for the Finite Element Discretization of Semilinear Parabolic non-Autonomous SPDEs Driven by multiplicative noise
Western Norway University of Applied Sciences（西挪威应用科学大学）；Center for Research in Computational and Applied Mechanics (CERECAM)（计算与应用力学研究中心）；Department of Mathematics and Applied Mathematics, University of Cape Town（开普敦大学数学与应用数学系）；The African Institute for Mathematical Sciences(AIMS) of South Africa（南非非洲数学科学研究院）；Fakultät für Mathematik, Technische Universität Chemnitz（开姆尼茨工业大学数学学院）
Strong convergence of some Magnus-type schemes for the finite element discretization of non-autonomous parabolic SPDEs driven by additive fractional Brownian motion and Poisson random measure
针对 fBm 与 Poisson 随机测度共同驱动的非自治半线性抛物型 SPDE，提出有限元结合随机 Magnus 型或半隐式 Euler 的全离散格式，并证明其强收敛阶。
Convergence analysis of the Magnus-Rosenbrock type method for the finite element discretization of semilinear non-autonomous parabolic PDEs with nonsmooth initial data
Western Norway University of Applied Sciences（西挪威应用科学大学）；University of Cape Town（开普敦大学）；Technische Universität Chemnitz（开姆尼茨工业大学）
