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    Fourth Order Runge Kutta method Detailed Step by Step Soln.

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    Question
    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 April 3, 2020, 4:36 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/fourth-order-runge-kutta-method-detailed-step-by-step-soln-121121

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    Solution:
    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 = ...

    Solution Summary

    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.

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