New Iterative Schemes In The Numerical Solution Of Two-Dimensional Time-Fractional Hyperbolic Partial Differentail Equations - Ali, Ajmal (2020)
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