TY - JOUR
T1 - A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 559
EP - 572
PY - 2012
DA - 2012/05
SN - 5
DO - http://doi.org/10.4208/nmtma.2012.m11032
UR - https://global-sci.org/intro/article_detail/nmtma/5949.html
KW - Evolution equation, weakly singular kernel, compact difference scheme, stability, convergence, numerical experiment.
AB - <p style="text-align: justify;">This paper is concerned with a compact difference scheme with the truncation error of order 3/2 for time and order 4 for space to an evolution equation with a weakly singular kernel. &nbsp;The integral term is treated by means of the second order convolution quadrature suggested by Lubich. The stability and convergence are proved by the energy method. A numerical experiment is reported to verify the theoretical predictions.</p>