RT info:eu-repo/semantics/article
T1 Integrating Semilinear Wave Problems with Time-Dependent Boundary Values Using Arbitrarily High-Order Splitting Methods
A1 Alonso Mallo, Isaías
A1 Portillo de la Fuente, Ana María
K1 65M12; 65M20; 65M22
K1 splitting methods; method of lines; initial boundary-value problem; consistency; convergence
K1 65M12; 65M20; 65M22
AB The initial boundary-value problem associated to a semilinear wave equation with time dependent boundary values was approximated by using the method of lines. Time integration isachieved by means of an explicit time method obtained from an arbitrarily high-order splittingscheme. We propose a technique to incorporate the boundary values that is more accurate than theone obtained in the standard way, which is clearly seen in the numerical experiments. We prove theconsistency and convergence, with the same order of the splitting method, of the full discretizationcarried out with this technique. Although we performed mathematical analysis under the hypothesisthat the source term was Lipschitz-continuous, numerical experiments show that this techniqueworks in more general cases.
PB MDPI Mathematics
YR 2021
FD 2021
LK https://uvadoc.uva.es/handle/10324/46787
UL https://uvadoc.uva.es/handle/10324/46787
LA eng
NO Mathematics. 2021; 9(10):1113. https://doi.org/10.3390/math9101113
DS UVaDOC
RD 01-may-2024