Laplace transforms are frequently used in the design of control structures for chemical engineering processes. In this paper, we have developed a novel numerical method to invert Laplace transforms, which involves a particular system of linear algebraic equations. We have proven that the error of our method is bounded, and the proposed formula asymptotically converges to the exact intended Laplace inverse function. A set of numerical simulations have been carried out to demonstrate the efficiency and reliability of our method. As a salient advantage, in addition to its high accuracy, our method requires the Laplace transform function to be defined only on the real axis.

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拉普拉斯变换的精确数值方法及其在过程动力学和控制中的应用

拉普拉斯变换通常用于化学工程过程的控制结构设计中。在本文中，我们开发了一种新颖的数值方法来对拉普拉斯变换进行求逆，其中涉及特定的线性代数方程组。我们已经证明了我们方法的误差是有界的，并且所提出的公式渐近收敛于精确的预期Laplace逆函数。进行了一组数值模拟，以证明我们方法的效率和可靠性。作为一个显着的优势，除了其高精度外，我们的方法还要求仅在实轴上定义拉普拉斯变换函数。