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Compared with the existing results, it has the advantage of providing a higher order accuracy, which may make it more efficient when aiming for a certain precision. Error estimations (depending on the controllability index of the system at the solution) are proved by using a recent result about stability of the optimal solution with respect to disturbances. Numerical results are provided which show the sharpness of the error estimations.<\/jats:p>","DOI":"10.1137\/16m1079142","type":"journal-article","created":{"date-parts":[[2018,1,5]],"date-time":"2018-01-05T16:03:49Z","timestamp":1515168229000},"page":"102-119","source":"Crossref","is-referenced-by-count":45,"title":["High Order Discrete Approximations to Mayer's Problems for Linear Systems"],"prefix":"10.1137","volume":"56","author":[{"given":"Alain","family":"Pietrus","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Teresa","family":"Scarinci","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vladimir","family":"Veliov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,1,5]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.3934\/naco.2012.2.547"},{"key":"atypb2","first-page":"104","volume":"287","author":"Alt W.","year":"2016","journal-title":"Appl. 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