i i i i i i i i i i i i i i i i i i i i y x f y f h w x f h w y x f h w w y y y

# I i i i i i i i i i i i i i i i i i i i y x f y f h w

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DERIVATION OF 2NDORDER RUNGE-KUTTA METHODS 5 OF 5 2921,1:solutionpossibleOnesolutionsinfiniteunknowns4withequations321and,21,1:equationsthreefollowingtheobtainweterms,Matching)(2),(),(...),(),()(:for expansionstwoderivedWe21222132122222111wwwwwwhOhyxfyfxfhyxfyyyxfyfhwxfhwyxfhwwyyyiiiiiiiiiiiii
2NDORDER RUNGE-KUTTA METHODS 3021and,21,1:thatsuch,,,Choose),(),(22212122111121wwwwwwKwKwyyKyhxfhKyxfhKiiiiii
ALTERNATIVE FORM 22111121),(),(KuttaeOrder RungSecondKwKwyyKyhxfhKyxfhKiiiiii3122111121),(),(FormeAlternativkwkwhyykhyhxfkyxfkiiiiii
CHOOSING , , W1AND W232CorrectorSinglea with'isThis),(),(221),(),(:becomesmethodKutta -eOrder RungSecond21,1then,1choosingexample,For 01121112121s Method HeunyxfyxfhyKKyyKyhxfhKyxfhKwwiiiiiiiiiii
CHOOSING , , W1AND W233MethodMidpointtheisThis)2,2()2,2(),(:becomesmethodKutta -eOrder RungSecond1,0,21then21Choosing12112121KyhxfhyKyyKyhxfhKyxfhKwwiiiiiiiii
2NDORDER RUNGE-KUTTA METHODS ALTERNATIVE FORMULAS 342111i2121211),(),()0(selectmulasKutta ForeOrder RungSecondKKyyKyhxfhKyxfhKiiiii211,21,:numbernonzeroany Pick1,21,21122122wwwwww
SECOND ORDER RUNGE-KUTTA METHOD EXAMPLE CISE301_Topic8L4&5 358269.32/)1662.018.0(42/)1()01.01(1662.0))01.()18.0(1(01.0),(18.0)1(01.0)4,1(:1STEP1,01.0,4)1(,1)(RK2using(1.02)findtosystemfollowingtheSolve2130201002302000132KKxxtxKxhtfhKtxxtfhKhxtxtxx
SECOND ORDER RUNGE-KUTTA METHOD EXAMPLE 366662.3)1546.01668.0(218269.321)01.1()01.001.1(1546.0))01.()1668.0(1(01.0

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• Spring '14