非線性拋物型方程組時間周期解的有限差分方法.pdf

1、華東師范大學(xué)碩士學(xué)位論文非線性拋物型方程組時間周期解的有限差分方法姓名：魏瑋申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：王元明20050501AbstractTimeperiodicbehaviorofsolutionsarisesfrommanyproblemsinvariousfieldofappliedsciences，suchasbiology，ecologybiochemistryandphysics，andmanyofthes

2、ephenomenaareusuallydescribedbyacoupledsystemofnonlinearparabolicequationsItisofcertainpracticalintereststogiveanefficientnumericalmethodforsuchsystemsInthispaper，afinitedifferencemethodwithhighaccuracyisestablishedforso

3、lvingtimeperiodicsolutionsofaclassofnonlinearparabolicsystemsinone—dimensionaldomainThismethodhassecondorderaccuracyintimeandfourthorderaccuracyinspaceSomequalitativeanalysesaregivenforthenonlinearfinitedifferenceschemeT

4、hisincludestheexistenceuniquenessoffinitedifferencesolutionandtheconvergenceofthefinitedifierencesolutiontotheanalyticalsolutionTosolvethenonlinearfinitedifferencescheme，anefficientmonotoneiterativealgorithmisdevelopedTh

5、esequencesofiterationsconvergemonotonicallytoanuniquesolutionofnonlinearfinitedifferencesystem，andtheinitialiterationcanbeexplicitlyconstructedwithoutanyknowledgeofthesolutionThenumericalresultsdemonstratetheadvantagesof

6、themethod，includingthemonotoneconvergencepropertyofiterativesequencesandthehighaccuracyofthemethodKeywords：nonlinearparabolicequations，time—periodicsolutions，finitedifferencemethod，highaecuracy1monotoneiteration，methodof