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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Consider the initial value problem: y'(1) = sin(t) – ty(1). y(0) = 1. %3D Use the improved Euler's method with 2 intervals to find an approximation for the so- lution on the interval (0, 1]. Round each step's answer to 4 significant digits and use the rounded value in the subsequent calculations.
Atel Solve the following initial value problems and find the interval of validity. y' = (1 − 2x)y², y(2) = 1/2. y' = x² (y + 2)(y − 2) ' y(1) = 1.
An investor has his savings invested in various investments. The amount at the end of each month, in the first semester, is shown in the table. a. Assuming that the rate of change of the amount can be represented by: y ′ (x) = (0.06y (x)) / x, obtain an approximation for the amount in the month of August, using the Improved Euler method, using h = 1 and initial condition given by the data for the month of June.b. What is the relative percentage error knowing that the particular solution of the PVI is y (x) = e ^ (0.06 lnx + 4.46).
x' = 10 t² x², x(0) = 3 Solve the above IVP and then find x(0.5). Put x(0.5) accurately calculated to the nearest thousandth (3 decimal places). Notation: dx and x = dt x' = x(t)
Consider the function f (x) = 3xe* = 0 the approximate solution with Newton-Raphson method for 1sxS2is: %3D a. Po = 1; p = 11.27422801 b. Po = 1.5; p = 1.2742280 C. Po = 1.5; p, = 1.27422801* 10-1 d. p = 1.27 e. Po = 1.5;p3 = 1.2742280 10-
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)~
The velocity dx/dt of a chemical reaction is proportional to (a-x), where x is the amount transferred in time t, and a is the concentration at time t=0 when x=0. Solve for a if the initial condition is x(0)=5.
Use Improved Euler's Method to approximate y(0.6) for y' y + x=0; y(0)=2 Use h=0.1. Calculate up to 7 decimal places. Round-off answer to 7 decimal places
d) Please provide a correct and well explained solution for the following;
Use Improved Euler's Method to approximate y(0.6) for y'+y=x−2=0; y(0)=2 Use h=0.1. Calculate up to 6 decimal places. Round-off answer to 6 decimal places
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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