NumericalMethodsforEvolutionaryDifferentialEquations(ComputationalScienceandEngineering)

Mathematicalmodelsinvolvingevolutionarypartialdifferentialequations(PDEs)aswellasordinarydifferentialequations(ODEs)ariseindiverseapplicationssuchasfluidflow,imageprocessingandcomputervision,physics-basedanimation,mechanicalsystems,relativity,earthsciences,andmathematicalfinance.Thistextdevelops,analyses,andappliesnumericalmethodsforevolutionary,ortime-dependent,differentialproblems.BothPDEsandODEsarediscussedfromaunifiedview.Theauthoremphasisesfinitedifferenceandfinitevolumemethods,specificallytheirprincipledderivation,stability,accuracy,efficientimplementation,andpracticalperformanceinvariousfieldsofscienceandengineering.Smoothandnon-smoothsolutionsforhyperbolicPDEs,parabolic-typePDEs,andinitialvalueODEsaretreated,andapracticalintroductiontogeometricintegrationmethodsisalsoincluded.Theauthorbridgestheoryandpracticebydevelopingalgorithms,concepts,andanalysisfrombasicprincipleswhilediscussingefficiencyandperformanceissues,anddemonstratingmethodsthroughexamplesandcasestudiesfromnumerousapplicationareas.