Anastasiya Onishkova

Chislennoe Issledovanie Zadach So Svobodnoy Granitsey Anastasiya Onishkova Russian edition

Matematicheskie modeli mnogikh fizicheskikh protsessov i yavleniy privodyat k kraevym zadacham matematicheskoy fiziki, soderzhashchim zaranee neizvestnye poverkhnosti, podlezhashchie opredeleniyu v khode resheniya zadachi. S takimi zadachami stalkivayutsya v promyshlennosti, stroitel'stve, v mashinostroenii, pri issledovanii problem iznosa i dolgovechnosti detaley i mnogikh drugikh oblastyakh. Primerami yavlyayutsya zadacha tayaniya l'da, razlichnye kontaktnye zadachi. Reshenie vozmozhno, kak pravilo, tol'ko chislenno, chto vyzyvaet znachitel'nye slozhnosti. Predlagayutsya chislennye algoritmy resheniya nekotorykh zadach matematicheskoy fiziki (odnomernykh i dvumernykh), zaklyuchayushchikhsya v opredelenii minimuma nekotorogo kvadratichnogo funktsionala, zadannogo v oblasti, soderzhashchey zaranee neizvestnuyu granitsu. Poslednyaya opredelyaetsya iz usloviya minimal'nosti funktsionala vmeste s neizvestnymi funktsiyami. Rassmotreny zadachi dlya ploskoy oblasti i dlya otrezka. Dlya poiska minimuma ispol'zovany razlichnye metody, v chastnosti, geneticheskie algoritmy. Privedeny primery resheniya. Rassmotrena vozmozhnost' ispol'zovaniya algoritma pri reshenii nekotorykh kontaktnykh zadach.