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.

翻译：本文提出并分析了用于半线性积分微分方程数值积分的指数梯形规则。尽管该方法为隐式格式，但可通过标准不动点迭代轻松获得数值解，从而简化其实现过程。在合理的假设条件下，我们在抽象希尔伯特空间框架中证明了该方法的时间二阶收敛性。数值实验验证了所证明的收敛阶次。