Ordinary Differential Equations (ODES) (CHAPTER 25 text book) 1. Solve the following problem over the interval from x=0

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Ordinary Differential Equations Odes Chapter 25 Text Book 1 Solve The Following Problem Over The Interval From X 0 1 (29.53 KiB) Viewed 8 times

Ordinary Differential Equations (ODES) (CHAPTER 25 text book) 1. Solve the following problem over the interval from x=0 to 1 using a step size of 0.25, where y(0) = 1. Display all your results on the same graph. dx (a) Analytically. Euler's method. (b) (c) Heun's method without iteration. Ralston's method. (d) Fourth-order RK method. 2. Use the (a) Euler and (b) Heun (without iteration) methods to solve -1+y=0 where y(0) = 2 and y'(0) = 0. Solve from x=0 to 4 using = 0.1. Compare the methods by plotting the solutions. The second-order ODE is transformed into a pair of first-order ODEs as in y(0)=2 di dz dt =t-y z(0)=0