Say you do two experiments where you apply one numerical method to approximate the solution of an initial value problem from t = 6 tot = 15, first using the stepsize At = h and then using the stepsize At = h/11 (so, taking 11 times more steps). If E¡ and E, are the errors in the respective approximations for y(15), what approximate number would you expect the ratio of the errors # to be if you were using the following numerical methods? (Alternatively: For the error in the second approximation, by approximately what factor would you expect the (global) truncation error of our first approximation to be cut?) Euler's method: Improved Euler's method: (Classical) 4th-order Runge-Kutta

Q: Use Euler's method and 4 steps to approximate y(1)

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Q: 3 [² (1 - – e¯²x) dx

A: Simpson's 3/8rule  ∫ydx=3h8y0+2(y3+y6+.....+yn-3)+3(y1+y2+....+yn-1)+yn  Where h is the interval…

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Q: If P(B) = 0.55, P(A | B) = 0.70, P(B')= 0.45, and P(A | B') = 0.90, find P(B | A). P(B|A) = (Round…

A: Given that PB=0.55,PA|B=0.70,PB'=0.45 and PA|B'=0.90.

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A: Given that, to study the relationship between Expenditure on Accommodation, $x and Expenditure on…

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A: x1 - x2 + 1 = 0  =>  x1 = x2 - 1  x12 + x22 = 4 =>  x2 = (4 - x12)1/2    x1(0) = 0.8, x2(0) =…

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Q: 12. If m/PSQ = (6x – 13)' and m/PQS = (x + 5)', find m/PQS.

A: In a triangle PQS,  Angle of SPQ=90 so, Angle PSQ + Angle PQS = 90 6x-13 + x+5 = 90 7x - 8 = 90  7x…

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A: Poisson Distribution :  The Poisson distribution is used to model the number of events occurring…

Q: apply 4th order Runge-Kutta to solve the following value problem y = x^2 + y for h = 0.1, y(1)=1 and…

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Q: f(-4) = 3, f'(-4) = 3, g(-4) = 4, gʻ(-4) = 8, calculate the following: (fg)'(-4) = (f/g)'(-4) =…

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Q: Using bisection and false-position method. Compute the solution of the following equation. a. y =…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: A student was solving the following problem. 81**2 -273 Step 1: (3*)*- = (3')* Step 2: 3**2 = 3 %3D…

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Q: X = y + % y = 0.000396707 – 0.24576 x2 22 = 0.00029753 - 0.12288 x²

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Q: Table 5.2.1). . (a) (c) -7/8 dx 10. (a) / Fdx (b) dx (c)

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Q: | f(x)dx = 12 and f(x)dx =3.1, then J f(x)dx =

A: Use formulas of limits of integration

Q: Solve by hand function bellow using Eu Repeat 5 times. (5 iterations)

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Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

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Q: stimate solutions of the following equation using a Graphical Estimation method. (You need to show…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.