Numerical Analysis/ODE Exercises

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Solve the following differential equations using the given method[edit | edit source]

Euler's Method[edit | edit source]

1) Solve differential equation y' = 3t2y in [0,1] using Euler's method with n=10,y(0)=1.

Runge-Kutta Second Order Method (RK2)[edit | edit source]

2) Solve differential equation y' = 2ty in [0,1] using RK2 method yn+1=yn+h/4(k1+3K2) where k1=f(tn,yn),k2=f(tn+2/3h,yn+2/3hk1)with n=5,y(0)=1.

Adams-Bashforth Two Step[edit | edit source]

3) Solve differential equation y' = 2ty in [0,1] using Two step Adams Bashforth method with n=5,y(0)=1.

Runge-Kutta Fourth Order (RK4)[edit | edit source]

4) Solve the ODE on the interval , using three steps of the Runge-Kutta 4 method with and .