2024/03/09 by Ostermann, Alexander, Vaisi, Nasrin
#45K05 #65M15 #65R20 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2403.05900
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point iteration, making its implementation straightforward. Second-order convergence in time is shown in an abstract Hilbert space framework under reasonable assumptions on the problem. Numerical experiments illustrate the proven order of convergence.