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CO2 Runge Kutta Method

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  Prepared   and presented by   :RINALYN   C. BELONIO  InourcareerweencounteredPartialDifferentialEquations(PDEs)andOrdinaryDifferentialEquations(ODEs)becauseitplaysimportantroleindesigningandmodelingproblemsofengineering.BasicapproachistouseanalyticmethodstosolveanODEorPDE,buttherearecaseswhichtheseanalyticsolutions won’t beenoughorsodifficultthatotherapproachesareneeded.ApowerfultoolforthesolutionofanordinarydifferentialequationistheRunge-KuttaMethod. Runge uttaMethod  This method was developed around 1900 by theGerman mathematicians Carl David Tolmé Runge andMartin Wilhelm Kutta. Theoreticallly, there are infinitely many fourth-order methods using four function values perstep. The method of Algorithm in Runge-Kutta is the most popular from a practical viewpoint because of its “symmetrical”  form and its simple coefficients. It was givenby Kutta himself. (Zeitschr, 1990) Carl David TolméRunge(1856-1927)Martin Wilhelm Kutta(1867-1944)  TheclassicalRunge-Kuttamethodisafourth-orderapproximation.Amethodusedtosolveordinarydifferentialequation(ODE)thatusesbetterapproximationthanthe Euler’s method.Thismethodprovidesanapproximatesolutionwithknowninitialconditions. Initial conditions: at x= x 0 , y= y 0
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