The exponential trapezoidal method for semilinear integro-differential equations
arxiv(2024)
摘要
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.
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