Using Python, Consider the following nonlinear initial value problem, du 2 dt = tu+2u with the initial condition u(0) = -5,0≤t≤5, and step size, h = 0. Using the implicit Euler method by deriving the recursion formula and by using Newton's method. Plot both solutions and along with the analytical result u(t) = -20e 2t 2t 9-5e +10te 2t

C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter14: Numerical Methods
Section14.3: Refinements To The Bisection Method
Problem 4E
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Using Python, Consider the following nonlinear initial value problem,
du 2
dt
= tu+2u
with the initial condition u(0) = -5,0≤t≤5, and step size, h = 0. Using the
implicit Euler method by deriving the recursion formula and by using
Newton's method.
Plot both solutions and along with the analytical result
u(t) =
-20e
2t
2t
9-5e +10te
2t
Transcribed Image Text:Using Python, Consider the following nonlinear initial value problem, du 2 dt = tu+2u with the initial condition u(0) = -5,0≤t≤5, and step size, h = 0. Using the implicit Euler method by deriving the recursion formula and by using Newton's method. Plot both solutions and along with the analytical result u(t) = -20e 2t 2t 9-5e +10te 2t
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