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The exponential trapezoidal method for semilinear integro-differential equations (2403.05900v1)
Published 9 Mar 2024 in math.NA and cs.NA
Abstract: 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.