DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

3rd Edition

ISBN: 9781119764564

Author: BRANNAN

Publisher: WILEY

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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 differentia…

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Textbook Question

Chapter 8.3, Problem 22P

In each of Problems 21 through 24, carry out one step of theEuler method and of the improved Euler method, using the step size h = 0.1 . Suppose that a local truncation error no

greater than 0.0025 is required. Estimate the step size that isneeded for the Euler method to satisfy this requirement at thefirst step.

y ' = 5 t − 3 y , y ( 0 ) = 2

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Chapter 8.3, Problem 21P

Chapter 8.3, Problem 23P

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For the following questions use h = 0.2. Also, clearly state all the values for xi’s and yi’s you would be using before each iteration. Adams-Bashforth Two-Step Method yi+1 =yi+(h/2) [3f(xi,yi)−f(xi−1,yi−1)] where i = 1, 2, ....N − 1. The local error is O(h^3) For the Adams-Bashforth two-step explicit method, use the Euler and the Trapezium rule as a predictor-corrector method with two iterations to obtain a starter value for y1. Use the Taylor series method with the appropriate number of terms to obtain another starter value for y1. For the above values for y1 compare with the exact value and comment on your result for each iteration. With your most accurate value for y1 found above, use the Adams- Bashforth Two-Step method to find the approximate value for the given differential equation at y2. Adams-Bashforth Three-Step Method yi+1 =yi + (h/12) [23f(xi,yi)−16f(xi−1,yi−1)+5f(xi−2,yi−2)] where i = 2, 3, ....N − 1. The local error is O(h^4) By using the exact…

1.Find the roots of the equation f(x) = x³ – x – 1 using xo = 1 %3D For 4 iteration by fixed points method

2.2 Solve y = x – y +1 for y(0) = 1 and x = 0(0.1)0.3 , using the Runge-Kutta method of order four. Work to four decimal

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DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

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