{"product_id":"automatic-control-for-adaptive-time-stepping-in-circuit-simulation-von-arie-verhoeven","title":"Automatic control for adaptive time stepping in circuit simulation","description":"\u003cp\u003eDAE-solvers are used to find the numerical solution  of the transient analysis of electrical circuits. For onestep methods, the local truncation error only depends on the last stepsize, but for multistep  methods, this error is also depends on previous stepsizes in a nonlinear way. Adaptive stepsize  control and order control can be used to control  these truncation errors. In connection with the articles of prof.S¿oderlind,  the possibilities of a control-theoretic approach  are investigated.  For onestep methods, the stepsize control process  can be viewed as a digital linear control system for  the logarithms of the errors and  steps. From a control-theoretic point of view, the  goal is to keep the error close to a reference level with use of the  stepsizes as input. If the stepsize control process  is correctly modelled, a finite order digital linear  controller can be designed.  From the results, it appears that it is  possible to design linear controllers that achieve  better properties than the commonly used deadbeat- controllers.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838387697\"\u003e\u003ch3\u003eNumerical mathematics applied to electronics\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783838387697","offer_id":39499034951773,"sku":"9783838387697","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/4892506d-e29d-4a72-910f-01fa3dff64d8.jpg?v=1770701124","url":"https:\/\/shop.autorenwelt.de\/en\/products\/automatic-control-for-adaptive-time-stepping-in-circuit-simulation-von-arie-verhoeven","provider":"Autorenwelt Shop","version":"1.0","type":"link"}