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Inventi Impact: Computational Mathematics

Articles

  • Inventi:ecm/17979/15
    A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary\nDifferential Equations (ODE) with Euler and Runge Kutta Methods
    01-Jan-1970 Research 2016 : January - March
    Md Amirul Islam

    ThispapermainlypresentsEulermethodandfourthorderRungeKuttaMethod(RK4)forsolving\ninitialvalueproblems(IVP)forordinarydifferentialequations(ODE).Thetwoproposedmethods\narequiteefficientandpracticallywellsuitedforsolvingtheseproblems.Inordertoverifytheac\ncuracy,wecomparenumericalsolutionswiththeexactsolutions.Thenumericalsolutionsarein\ngood agreement with the exact solutions. Numerical comparisons between Euler method and\nRungeKuttamethodhavebeenpresented.Alsowecomparetheperformanceandthecomputa\ntional effort of suchmethods. In order to achieve higher accuracy in the solution, the step size\nneedstobeverysmall.Finallyweinvestigateandcomputetheerrorsofthetwoproposedmeth\nodsfordifferentstepsizestoexaminesuperiority.Severalnumericalexamplesaregiventodem\nonstratethereliabilityandefficiency.

    How to Cite this Article
    CC Compliant Citation: Islam, Md.A. (2015) A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for\nOrdinary Differential Equations (ODE) with Euler and Runge Kutta Methods. American Journal of Computational Mathematics,\n5, 393404. http://dx.doi.org/10.4236/ajcm.2015.53034, http://creativecommons.org/licenses/by/4.0/.
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