Consider the initial value problem given below.dx-=1+tsin (tx), x(0) = 0dtUse the improved Euler's method with tolerance to approximate the solution to this initial value problem at t= 0.8. Fora tolerance of ε = 0.01, use a stopping procedure based on absolute error.The approximate solution is x(0.8) ~(Round to three decimal places as needed.)

The given initial value problem dxdt=1+tsintx, x0=0. Using the improved Euler's method we have to…

Answered: Consider the initial value problem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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21.1 f(x)=S0pi/2(8+4cos(x))dx Solve using multiple-application trapezoid rule, with n= 2 and 4.
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = x² + y², y(0) = 3; y(0.5) (h = 0.1) (h = 0.05) y(0.5) ≈ y(0.5)~
d) Please provide a correct and well explained solution for the following;
Use the improved Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = xy2 − y/x, y(1) = 2; y(1.5)
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