The dynamics of the variable y with respect to variable x is described by the following ODE: dy –x²y – 1.2x² = 0 dx where y(0)=1 The exact solution is given as: у(x) %3D 2.2 еxp°. 0.3333x2 -1.2 Use a fourth-order Runge-Kutta (RK4) numerical algorithm for solving the ODE to find the value of y(0.945), using 3 integration steps. Compare your calculated result with the exact solution and calculate the minimum number of correct significant digits in your answer.
The dynamics of the variable y with respect to variable x is described by the following ODE: dy –x²y – 1.2x² = 0 dx where y(0)=1 The exact solution is given as: у(x) %3D 2.2 еxp°. 0.3333x2 -1.2 Use a fourth-order Runge-Kutta (RK4) numerical algorithm for solving the ODE to find the value of y(0.945), using 3 integration steps. Compare your calculated result with the exact solution and calculate the minimum number of correct significant digits in your answer.
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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Transcribed Image Text:The dynamics of the variable y with respect to
variable x is described by the following ODE:
dy
–x²y – 1.2x² = 0
dx
where y(0)=1
The exact solution is given as:
у(x) %3D 2.2 еxp°.
0.3333x2
-1.2
Use a fourth-order Runge-Kutta (RK4)
numerical algorithm for solving the ODE to
find the value of y(0.945), using 3 integration
steps.
Compare your calculated result with the exact
solution and calculate the minimum number
of correct significant digits in your answer.
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