R-K-1Quiz 6 Single Ordinary Differential Equation (1ODE)

Solve following ODE using 1st, 2nd, 4th order Runge-Kutta, Predictor-Corrector as well as the analytical Method.

with initial condition

The solution can be sarted from t = 0 up to t = 0.5 with Dt = 0.1 (or h). Give the value of y(0.5) for both analytical and numerical solution, give your comments !

DIKETAHUI:JAWAB:Tabel Runge-Kutta Orde 1tnynh f(t,y)yn+1010-280.18-1.66.40.26.4-1.285.120.35.12-1.0244.0960.44.096-0.81923.27680.53.2768-0.655362.62144

R-K-2Runge-Kutta Orde 2:tnynk1 k2yn+1010-2-1.68.20.18.2-1.64-1.3126.7240.26.724-1.3448-1.075845.513680.35.51368-1.102736-0.88218884.52121760.44.5212176-0.90424352-0.7233948163.7073984320.53.707398432-0.7414796864-0.59318374913.0400667142

R-K-4RUNGE-KUTTA ORDE 4tnynk1 k2k3k4yn+1010-2-1.8-1.82-1.6368.18733333330.18.1873333333-1.6374666667-1.47372-1.4900946667-1.33944773336.70324271110.26.7032427111-1.3406485422-1.206583688-1.2199901734-1.09665050755.4881682490.35.488168249-1.0976336498-0.9878702848-0.9988466213-0.89786432554.49334628440.44.4933462844-0.8986692569-0.8088023312-0.8177890238-0.73511145213.67885238130.53.6788523813-0.7357704763-0.6621934286-0.6695511334-0.60186024963.0119990729

P-KPREDIKTOR-KOREKTOR00.10.20.30.40.5Iterasiynf(tn,yn)yn+1*f(tn+1,yn+1)yn+1f(tn,yn)yn+1*f(tn+1,yn+1)yn+1f(tn,yn)yn+1*f(tn+1,yn+1)yn+1f(tn,yn)yn+1*f(tn+1,yn+1)yn+1f(tn,yn)yn+1*f(tn+1,yn+1)yn+1010-208-168.2-16.46.56-13.126.724-13.4485.3792-10.75845.51368-11.027364.410944-8.8218884.5212176-9.04243523.61697408-7.233948163.707398432110-208-16.48.18-16.366.544-13.4486.6896-13.37925.35168-11.027365.469272-10.9385444.3754176-9.04243524.47022304-8.940446083.576178432-7.4147968643.6524608928210-208-16.368.182-16.3646.5456-13.37926.69484-13.389685.355872-10.9385445.4784288-10.95685764.38274304-8.940446084.483563616-8.9671272323.5868508928-7.30492178563.6699611651310-208-16.3648.1818-16.36366.54544-13.389686.694136-13.3882725.3553088-10.95685765.47687952-10.953759044.381503616-8.9671272324.4808352064-8.96167041283.5846681651-7.33992233023.6657555692410-208-16.36368.18182-16.363646.545456-13.3882726.6942244-13.38844885.35537952-10.953759045.477114008-10.9542280164.3816912064-8.96167041284.4813190866-8.96263817313.5850552692-7.33151113853.666611621510-208-16.363648.181818-16.3636366.5454544-13.38844886.69421376-13.388427525.355371008-10.9542280165.4770809832-10.95416196644.3816647866-8.96263817314.4812409762-8.96248195243.584992781-7.3332232423.6664557165610-208-16.3636368.1818182-16.36363646.54545456-13.388427526.694215004-13.3884300085.3553720032-10.95416196645.4770854053-10.95417081064.3816683242-8.96248195244.4812527671-8.96250553433.5850022137-7.3329114333.6664819188710-208-16.36363648.18181818-16.363636366.545454544-13.3884300086.6942148616-13.38842972325.3553718893-10.95417081065.4770848349-10.95416966984.3816678679-8.96250553434.4812510747-8.96250214943.5850008598-7.33296383753.6664777754810-208-16.363636368.181818182-16.3636363646.5454545456-13.38842972326.6942148776-13.38842975535.3553719021-10.95416966985.4770849064-10.95416981284.3816679251-8.96250214944.4812513083-8.96250261663.5850010466-7.33295555073.6664783999910-208-16.3636363648.1818181818-16.36363636366.5454545454-13.38842975536.6942148759-13.38842975175.3553719007-10.95416981285.4770848976-10.95416979534.3816679181-8.96250261664.481251277-8.96250255413.5850010216-7.33295679983.66647830931010-208-16.36363636368.1818181818-16.36363636366.5454545455-13.38842975176.6942148761-13.38842975215.3553719008-10.95416979535.4770848987-10.95416979744.3816679189-8.96250255414.4812512811-8.96250256223.5850010249-7.33295661873.66647832211110-208-16.36363636368.1818181818-16.36363636366.5454545455-13.38842975216.694214876-13.38842975215.3553719008-10.95416979745.4770848986-10.95416979714.3816679188-8.96250256224.4812512806-8.96250256123.5850010245-7.33295664413.66647832031210-208-16.36363636368.1818181818-16.36363636366.5454545455-13.38842975216.694214876-13.38842975215.3553719008-10.95416979715.4770848986-10.95416979714.3816679189-8.96250256124.4812512807-8.96250256133.5850010245-7.33295664073.66647832061310-208-16.36363636368.1818181818-16.36363636366.5454545455-13.38842975216.694214876-13.38842975215.3553719008-10.95416979715.4770848986-10.95416979714.3816679189-8.96250256134.4812512806-8.96250256133.5850010245-7.33295664113.66647832051410-208-16.36363636368.1818181818-16.36363636366.5454545455-13.38842975216.694214876-13.38842975215.3553719008-10.95416979715.4770848986-10.95416979714.3816679189-8.96250256134.4812512807-8.96250256133.5850010245-7.33295664113.6664783205DIKETAHUI:Hasil Prediktor-korektortnyn0100.18.1818181820.26.69421487610.35.47708489870.44.48125128070.53.6664783206

ANALITIKCARA ANALITIKTABEL HASIL ANALITIKDIKETAHUI:tnyn0100.18.18730753080.26.70320046040.35.48811636090.44.49328964120.53.6787944117

RANGKUMANNAMA:KARTINIPERBANDINGAN HASIL (y) dari perhitungan R-K ORDE 1,2,4 DAN P-K SERTA ANALITIKNIM:2213005

tnR-K-1R-K-2R-K-4P-KANALITIK010101010100.188.28.18733333338.1818181828.18730753080.26.46.7246.70324271116.69421487616.7032004600.35.125.513685.4881682495.47708489875.48811636090.44.0964.52121764.49334628444.48125128074.49328964120.53.27683.7073984323.67885238133.66647832063.6787944117comment:semakin tinggi orde pada perhitungan Runge-Kutta maka semakin akurat perhitungannya yaitu pada R-K-4 hasilnya mendekati perhitungan analitikbegitu pula dengan perhitungan Predictor-corrector juga akurat dengan hasil yang mendekati perhitungan analitik.