Use the classical fourth order RK method to integrate (a) f(x, y) = -2x3 +12x2 - 20x + 8.5 using a step size of h = 0.5 and an initial condition of y = 1 at x = 0.

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Q: Explain and derive the fourth order Runge Kutta method in detail

A:

Q: Find the slopes of fourth order Runge Kutta method.

A: We need to find the slopes of fourth order Runge Kutta method.

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Q: Given F(x)=x^2-209 , a=4 ,b=15 Find C1,C2,C3,C4,C5, by bisection method?

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Q: NRT plz check my cu feuhelon n'a qu-A 1. x0.082 tahn (10127BK) 0 מףב.ף 1.2gchy x Imot Tgch,

A: The calculation is shown in the following step.

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Q: Derive third order Runge-Kutta method.

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Q: (a) The matriz 1 3 -1 0 5 3 0 2 is invertible. Find A- by any method you know.

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A: Integrate the following.                                ∫ 1x+x dx

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Q: F (x) = x + 4x2 - 10 = 0 [1,2]

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Q: Derive fourth order Runge-Kutta Method.

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Q: f(x) = x - e-x?

A: Use bisection method to find a root.

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Q: X1 + x2 + x3 = 6 2х, — х2 + 4xз %3D 12 X2 + 4x3 -Зх, + 2х2 — хз — — 4 X3

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Q: Derive the formula of of fourth order Runge kutta method completely.

A: Assume first order differential equation, dydx=fx,y,y0=y0