TY - JOUR
T1 - A High-order Exponential Integrator for Nonlinear Parabolic Equations with Nonsmooth Initial Data
AU - Li, Buyang
AU - Ma, Shu
N1 - This work is partially supported by the Hong Kong Research Grants Council (GRF project No. 15300519) and an internal grant of the university (project code ZZKK)
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.
PY - 2021/4
Y1 - 2021/4
N2 - A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach, the exponential k-step method would have kth-order convergence in approximating a mild solution, possibly nonsmooth at the initial time. In consistency with the theoretical analysis, a numerical example shows that the method can achieve high-order convergence in the maximum norm for semilinear parabolic equations with discontinuous initial data.
AB - A variable stepsize exponential multistep integrator, with contour integral approximation of the operator-valued exponential functions, is proposed for solving semilinear parabolic equations with nonsmooth initial data. By this approach, the exponential k-step method would have kth-order convergence in approximating a mild solution, possibly nonsmooth at the initial time. In consistency with the theoretical analysis, a numerical example shows that the method can achieve high-order convergence in the maximum norm for semilinear parabolic equations with discontinuous initial data.
KW - Discontinuous initial data
KW - Exponential integrator
KW - High-order accuracy
KW - Nonlinear parabolic equation
KW - Nonsmooth initial data
KW - Variable stepsize
UR - https://www.scopus.com/pages/publications/85102111438
UR - https://link.springer.com/article/10.1007/s10915-021-01438-7
U2 - 10.1007/s10915-021-01438-7
DO - 10.1007/s10915-021-01438-7
M3 - Journal article
AN - SCOPUS:85102111438
SN - 0885-7474
VL - 87
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
M1 - 23
ER -
