Use Runge-Kutta method of order four to approximate the solution to the given initial value problem and compare the results to the actual values.
y'=e^(t-y) , 0 <=t <=1 , y(0)=1 with h = 0.5(Interval)
Actual solution is y(t)= In((e^t+e-1).
For full description of the problem, please see the attached question file.© BrainMass Inc. brainmass.com March 21, 2019, 2:21 pm ad1c9bdddf
For the first interval of h = 0.5 we get as below (for step by step explanation please see the attached solution file)
k1=0.183940 , k2=0.215430 , k3= 0.212065 , k4 = ...
This solution is comprised of detailed explanation of using Runge Kutta method of order four to solve Ordinary Differential Equations(Initial Value Problems). Formulas included in standard notation and the solution is explained in easy to understand format. The attached solution file contains 5 pages in which each minute detail regarding the solution is given.
Students would be able to solve other problems on this topic easily with the help of this solution.
Thanks for using Brainmass.com. Have a great day.