At the 1940s Manhattan project, back when computer meant a job: "person who computes mathematical statements", major advancements were made in the integration of hyperbolic PDEs, by substituting electro-mechanical and then vacuum-tube machines to do the job. You know, those hard-wired vacuum tube monsters like ENIAC.
You could argue that the First useful thing electronic computers did was integration...
https://www.tandfonline.com/doi/full/10.1080/00295450.2021.1...