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Metode Liejevih grup in parcialne diferencialne enačbe : magistrsko delo
Perne, Andrej, 1979-
Opišemo konstrukcijo Magnusovih metod za reševanje linearnih navadnih diferencialnih enačb na Liejevih grupah ter štirih razredov metod Liejevih grup za reševanje nelinearnih navadnih diferencialnih ...enačb na Liejevih grupah. Rešitve s temi metodami v nasprotju z rešitvami z metodami Runge-Kutta ohranjajo ivariante, ki se ohranjajo pri točni rešitvi, prav tako pa dobimo z njimi bolj natančne rezultate, kar preverimo na zgledih, ki so vključeni v magistrsko delo. Te metode nato uporabimo pri reševanju nekaterih linearnih in nelinearnih parcialnih diferencialnih enačb. Te najprej semidiskretiziramo, da dobimo sistem navadnih diferencialnih enačb, ki je lahko linearen ali pa nelinearen, nato pa ga rešimo z ustrezno metodo Liejevih grup. Na numeričnih zgledih si ogledamo delovanje tega postopka, pri katerem smo konstruirali metode četrtega reda.
Type of material - master's thesis
; adult, serious
Publication and manufacture - Ljubljana : [M. Perne], 2006
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