The flow invariant for the nonlinear system
Not what you're looking for?
Please solve the following numerical analysis problem:
Determine the flow Qt : R^2 into R^2 for the nonlinear system: x' =f(x) with
f(x) = [ -x1 ]
[ x1^2 + 2x2 ]
and show that the set S = { x E R^2l x2 = -x^2/4 } is invariant with respect to the flow {Qt}.
Please use the step by step method to show the solution.
Purchase this Solution
Solution Summary
This posting provides a solution to a first order linear differential equation initial value problem. It provides a step by step method with the calculations for the flow invariant for a nonlinear system.
Solution Preview
See the attached file.
Problem: Determine the flow Qt : R^2 into R^2 for the nonlinear system: x' =f(x) with
f(x) = [ -x1 ]
[ x1^2 + 2x2 ]
and show that the set S = { x E R^2l x2 = -x^2/4 } is invariant with respect to the flow {Qt}.
Solution:
Determine Qt:
Start by solving: x1' = -x1 => x1 = Ce^-t.
Plug that result into x2' = x1^2 + 2x2 and solve for x2.
x2' = ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.