Convert the equation d'y dy -3 x y 0 -3. dx3 dx and initial conditions y(0)= 1.11983, y' (0)=0.83697 and y"(0)30.12356, into three first order differential equations. Find the formulas for solving this system of equations by: 1. Euler's forward difference method 2. The second order Runge-Kutta method based on k, =h f(x,,Yn) k2 = h f(x, +h/2,yn+k,/2) Yn +1=Yn+ k2 Find the numerical solution y at x=0.1, x=0.2 and x 0.3 by both methods using a step length h =0.1. Give your answers to 5 decimal places (no more and no less) however you should do you calculations with sufficient accuracy to ensure you answers are accurate to 5 decimal places. For the Euler method: Yo = 1.11983 Y1 y2= Y3 = For the Runge-Kutta method: Yo = 1.11983 Y1 Y2 Y3 =
Convert the equation d'y dy -3 x y 0 -3. dx3 dx and initial conditions y(0)= 1.11983, y' (0)=0.83697 and y"(0)30.12356, into three first order differential equations. Find the formulas for solving this system of equations by: 1. Euler's forward difference method 2. The second order Runge-Kutta method based on k, =h f(x,,Yn) k2 = h f(x, +h/2,yn+k,/2) Yn +1=Yn+ k2 Find the numerical solution y at x=0.1, x=0.2 and x 0.3 by both methods using a step length h =0.1. Give your answers to 5 decimal places (no more and no less) however you should do you calculations with sufficient accuracy to ensure you answers are accurate to 5 decimal places. For the Euler method: Yo = 1.11983 Y1 y2= Y3 = For the Runge-Kutta method: Yo = 1.11983 Y1 Y2 Y3 =
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:Convert the equation
d®y
dy
-3·
-3 x y 0
dx3
dx
and initial conditions y(0)= 1.11983, y'(0)= 0.83697 and y"(0)= 0.12356, into three first order
differential equations. Find the formulas for solving this system of equations by:
1. Euler's forward difference method
2. The second order Runge-Kutta method based on
k, =h f(x,,Yn)
k2 = h f(x, +h/2,yn+k,/2)
Yn+1=Yn+ k2
Find the numerical solution y at x=0.1, x=0.2 and x 0.3 by both methods using a step length
h =0.1.
Give your answers to 5 decimal places (no more and no less) however you should do you calculations
with sufficient accuracy to ensure you answers are accurate to 5 decimal places.
For the Euler method:
Yo = 1.11983
Y2=
Y3 =
For the Runge-Kutta method:
Yo = 1.11983
Y2 =
Y3 =
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