New Iterative Schemes In The Numerical Solution Of Two-Dimensional Time-Fractional Hyperbolic Partial Differentail Equations
In literature,numericalschemessuchasfinitedifferencemethod,finiteelement method, finitevolumemethod,boundaryelementmethodandspectralmethodshave been utilizedforthediscretizationofmanytypesofFractionalDifferentialEquations (FDEs). SuchtypesofmethodsleadFDEsintoalargeandsparsesystemofsimul- taneou...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | http://eprints.usm.my/54826/1/AJMAL%20ALI%20-%20TESIS%20cut.pdf |
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| Summary: | In literature,numericalschemessuchasfinitedifferencemethod,finiteelement
method, finitevolumemethod,boundaryelementmethodandspectralmethodshave
been utilizedforthediscretizationofmanytypesofFractionalDifferentialEquations
(FDEs). SuchtypesofmethodsleadFDEsintoalargeandsparsesystemofsimul-
taneous linearequationswhichcanbesolvedbyiterativemethodsthatarebasedon
the point-orientediterationschemesonthewholediscretizationdomain Wh, where h is
the gridspacinginboth x and y directions. Inallsuchtypeofiterativemethods,large
arithmetical operationsarerequiredforconvergence,becausepreviousvalueshaveto
be storediftherecentvalueistobecalculated.Overthepastdecades,manyschol-
ars andresearchershaveestablishednumerousproficientfastalgorithmstoreducethe
computation cost.Theincreasingdemandforadvancedresolutionsimulationsinless
computer timehavecontinuouslychallengedtheresearcherstocomeupwithmore
effective,well-organizedandfastcomputationalalgorithmsinsolvingtheFDEs.One
of thewaystoachievefasterconvergenceisbytheutilizationofgroupiterativemeth-
ods whicharebasedongroup-orientediterationschemesthatutilizelessthan h |
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