Matemātiskās fizikas problēmu ar periodiskiem robežnosacījumiem matemātiskā modelēšana

6533b860fe1ef96bd12c340d

RESEARCH PRODUCT

Matemātiskās fizikas problēmu ar periodiskiem robežnosacījumiem matemātiskā modelēšana

Aigars Gedroics

subject

Fizika materiālzinātne matemātika un statistika Matemātika

description

Darbā izstrādāti jauni speciāli algoritmi parasto un parciālo diferenciālvienādojumu problēmu ar periodiskajiem nosacījumiem skaitliskai modelēšanai, kuri balstās uz precīzā spektra izmantošanu telpisko parciālo atvasinājuma aproksimēšanai ar galīgajām diferencēm. Algoritmi tiek veidoti dažādām divdimensiju matemātiskās fizikas problēmām (lineārām un nelineārām), balstoties uz taišņu metodes algoritmiem un precīzā spektra diferenču shēmām. Izveidotie algoritmi tiek realizēti un salīdzināti ar datorprogrammas MATLAB palīdzību. Ar iegūtajiem algoritmiem tiek risinātas vairākas lietišķas problēmas, t.sk 2D magnetohidrodinamiska plūsma ap periodiski novietotiem cilindriem, 2D plūsma cilindrā ārējā magnētiskā lauka ietekmē un metāla koncentrācija kūdras slāņos. Atslēgvārdi: periodiski robežnosacījumi, cikliskas matricas, galīgo diferenču shēma, galīgo diferenču shēma ar precīzo spektru.

year	journal	country	edition	language
2014-01-01

https://dspace.lu.lv/dspace/handle/7/4093

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