2070.兩類隨機(jī)rungekutta方法的線性穩(wěn)定性分析

1、學(xué)校代碼：10270分類號(hào)：024學(xué)號(hào)：142200616碩士學(xué)位論文兩類隨兩類隨機(jī)RungeKuttRungeKutta方法的線性穩(wěn)方法的線性穩(wěn)定性分析定性分析學(xué)院：數(shù)理學(xué)院專業(yè)：計(jì)算數(shù)學(xué)研究方向：隨機(jī)微分方程數(shù)值解研究生姓名：鐘娟指導(dǎo)教師：郭謙副教授完成日期：二零一七年三月英文摘要上海師范大學(xué)碩士學(xué)位論文AbstractMostofstochasticdelaydifferentialequationscannotbesolveda

2、nalyticallysothatnumericalmethodsareoneoftheimptantwaystoinvestigatethedynamicsofitssolution.AsweknowRungeKuttamethodisusuallyappliedtosolvingstochasticdifferentialequation.Ontheotherhthestabilityofanexplicitnumericalsch

3、emeisnotasgoodastheimplicitonebuttheexplicitonehasbettercomputationalefficiency.FurtherakindofexplicitRungeKuttamethodbasedonChebyshevpolynomialshowsgoodstabilitypropertiesHoweverthestabilitydomainofthemethodwillshrinkto

4、zeroinsomeplaces.InadditionhaveakindofexplicitRungeKuttamethodbasedonLegendrepolynomialalsoshowsgoodstabilitypropertiesthereisnosuchproblemitsstabilitydomaincanbeextendedbyincreasingthestagenumberoftheRungeKuttamethod.Fs

5、tochasticdifferentialequationsThisarticlefirststudythattheexplicitstochasticRungeKuttaLegendremethodConstructtwokindsoffmatwhichthederofconvergencerespectivelyis12der1deranalyzethatthelinearmeansquarestabilityofthesemeth

6、odsgetthemeansquarestabilitycriterionconditionsOurtheyisverifiedbynumericalexamples.TheninviewofthestochasticdelaydifferentialequationswewillstudythatthealmostsureexponentialstabilityofanexplicitstochasticRungeKuttaCheby

7、shev(SROCK)methodwhichisanalyzedbyapplyingthetechniquesbasedinadiscretesemimartingaleconvergencethem.KeyWds:stochasticdifferentialequationsRungeKuttaLegendremethodsRungeKuttaChebyshevmethodsmeansquarestabilityalmostsuree