Geodesic
An exponential integrator for non-autonomous parabolic problems
Electronic transactions on numerical analysis, Tome 41 (2014), pp. 497-511
For the time integration of non-autonomous parabolic problems, a new type of exponential integrators is presented and analyzed. The construction of this integrator is closely related to general construction principles of the continuous evolution system. The proximity to the continuous problem allows one to obtain a third-order method that does not suffer from order reduction. The stated order behavior is rigorously proved in an abstract framework of analytic semigroups. The numerical behavior of the integrator is illustrated with an example that models a diffusion process on an evolving domain. Comparisons with an implicit Runge-Kutta method of order three and a standard fourth-order Magnus integrator are given.
Classification : 65M12, 65L06
Keywords: exponential integrators, parabolic problems, time-dependent operators, evolving domains 
@article{ETNA_2014__41__a0,
     author = {Hipp,  David and Hochbruck,  Marlis and Ostermann,  Alexander},
     title = {An exponential integrator for non-autonomous parabolic problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {497--511},
     year = {2014},
     volume = {41},
     zbl = {1312.65210},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2014__41__a0/}
}
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Hipp,  David; Hochbruck,  Marlis; Ostermann,  Alexander. An exponential integrator for non-autonomous parabolic problems. Electronic transactions on numerical analysis, Tome 41 (2014), pp. 497-511. http://geodesic.mathdoc.fr/item/ETNA_2014__41__a0/