Question

In: Computer Science

develop a vba computer code to solve the initial value first ODE:dy/dt =(4y)/t with the initial...

develop a vba computer code to solve the initial value first ODE:dy/dt =(4y)/t with the initial condition of y (1)=2 with a time step of 0.05 for the time interval 1 <=t<= 2 for the euler method,2nd order runge-kutta method and the 4th order runge-kutta method

Expert Solution

Given DE =

The eulers formula is given by

the initial value t₀ and y₀ are given as 1 and 2 respectively.

Using Excel sheet solving for t.

The modified Eulers method also known as Runge Kutta method of second order.

The formula is given by

where

Now using Runge Kutta method of fourth order we have

Where

Where , , , .

Since =0.05 the step size is small the accuracy increases.

Using Excel spread sheets computing the values by all the three methods.

venereology answered 9 months ago

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