Ali, Ajmal
(2020)
New Iterative Schemes In The Numerical Solution Of Two-Dimensional Time-Fractional Hyperbolic Partial Differentail Equations.
PhD thesis, Universiti Sains Malaysia.
Abstract
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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