New Iterative Schemes In The Numerical Solution Of Two-Dimensional Time-Fractional Hyperbolic Partial Differentail Equations
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Date
2020-07
Authors
Ali, Ajmal
Journal Title
Journal ISSN
Volume Title
Publisher
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 hô€€€2=2
or hô€€€2=4 (dependingonthemethodused)iterativepointsofthespatialdomain.
Description
Keywords
Numerical Solution , Two-Dimensional Time