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dy/dt= 1 + t2 + y,  y(1) = -4 Above shows the Ordinary Differential Equation(ODE).Use the below methods to solve the ODE above to determine y(1.01), y(1.02) & y(1.03) with step size h=0.01 a.2nd order Taylor series b.Euler method but also generate a table & perform a calculation of the error-based on the exact results gotten.

dy/dt= 1 + t2 + y,  y(1) = -4 Above shows the Ordinary Differential Equation(ODE).Use the below methods to solve the ODE above to determine y(1.01), y(1.02) & y(1.03) with step size h=0.01 a.2nd order Taylor series b.Euler method but also generate a table & perform a calculation of the error-based on the exact results gotten.

Advanced Engineering Mathematics
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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dy/dt= 1 + t2 + y,  y(1) = -4

Above shows the Ordinary Differential Equation(ODE).Use the below methods to solve the ODE above to determine y(1.01), y(1.02) & y(1.03) with step size h=0.01
a.2nd order Taylor series
b.Euler method but also generate a table & perform a calculation of the error-based on the exact results gotten.

Expert Solution
Step 1

Formula to be used:

(a) Second order Taylor's polynomial for a function y(t) about t = a is given by

P2(t)=ya+t-ay'a+t-a22y''a

 

(b) Euler's method give an approximate value of the function y=f(t, y) at x = xn+1 by the formula

yn+1=yn+hftn,yn

Here h is the step size.

 

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