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RK4 method 1.consider the initial value problem y’=2y,y(0)=1 the analytic solution is y(x)=e^2x a. Approximate y(0.1)using one step of the fourth order Runga-Kutta method. b. Find a bound for the local truncation error in y1 c. Compare the error in y1 with your errror bound.

RK4 method

1.consider the initial value problem

y’=2y,y(0)=1

the analytic solution is y(x)=e^2x

a. Approximate y(0.1)using one step of the fourth order Runga-Kutta method.

b. Find a bound for the local truncation error in y1

c. Compare the error in y1 with your errror bound.

2. Euler’s method for systems

Consider the initial value problem

y”-y=0,y(0)=1,y'(0)=1

a. Write the problem as a system of first order differential equations.

b. Apply two step of Euler’s method with h=0.1 to the system for approximating y(0.2)

3.Consider the system

dx/dt=6x-2x^2-xy

dy/dt=6y-2y^2-xy

a. Find and classify all critical points

4.The improved Euler’s method

Use the improved Euler’s method with step 0.1 to approximate the solution to the intial-value problem

y’=x-y^2,y(1)=0 at x=1.1 and x=1.2

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