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Improved Euler’s Method. 3 조 강다연 김만선 박진원 박효식. CONTENTS. Euler’s method Improved Euler’s method Problem 1 & 2 Summary Application. Euler’s Method. Consider the initial value problem . Approximation by a rectangle. Improved Euler’s Method.
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Improved Euler’s Method 3조 강다연 김만선 박진원 박효식
CONTENTS • Euler’s method • Improved Euler’s method • Problem 1 & 2 • Summary • Application
Euler’s Method Consider the initial value problem Approximation by a rectangle
Improved Euler’s Method A more accurate way of approximating the integral is by finding the area of a trapezoid obtained by joining the points
Improved Euler’s Method Approximation by a trapezoid
Problem 1 Compute the improved Euler`s method approximation to the solution (x)= of at using step size of ,,,
Problem 1 Improved Euler’s Value
Problem 1 Improved Euler h=1 Improved Euler h=
Problem 1 Improved Euler h= Improved Euler h=
Problem 1 Euler’s vs Improved Euler’s
Problem 1 Euler’s vs Improved Euler’s
Problem 1 Euler & Improved Euler h=1 Euler & Improved Euler h=
Problem 1 Improved Euler’s vs Euler’s () Randomly
Problem 2 Use the improved Euler’s method with tolerance of to approximate the solution to the initial value problem at
Problem 2 Bisection()
Problem 2 Ten Power () Random ()
Summary • Euler vs Improved Euler Improved Euler is much superior (less iteration) → We can justify Big Oh notation
