Find the Error: Modifying Euler's Method for Initial Condition y(5)=3

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SUMMARY

This discussion focuses on modifying Euler's method to accommodate the initial condition y(5)=3 for the differential equation y'=1+t. The participants detail the application of a time step of 0.1 to compute the approximate value of y(5.4) using this modified method. Additionally, they emphasize the importance of calculating the exact solution through calculus to determine the percentage error of Euler's method in this context.

PREREQUISITES
  • Understanding of Euler's method for numerical solutions of differential equations
  • Basic calculus for finding exact solutions of differential equations
  • Familiarity with error analysis in numerical methods
  • Knowledge of differential equations, specifically first-order equations
NEXT STEPS
  • Learn how to implement Euler's method in Python using libraries like NumPy
  • Study the Runge-Kutta methods for improved accuracy in numerical solutions
  • Explore error estimation techniques for numerical methods
  • Investigate other initial conditions and their impact on numerical solutions
USEFUL FOR

Students and professionals in mathematics, engineering, and computer science who are interested in numerical methods for solving differential equations and analyzing their accuracy.

mvgio124
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Euler's method?

Describe how to modify Euler's method to deal with the initial condition of y(5)=3 instead of y(0)=3.

Use this on the equation y'=1+t using a time step of 0.1 and initial condition of y(5)=3 and find y(5.4) .
??

Now find the exact solution of this equation using calculus and find what the exact answer is.

= ?
What is the percentage error in the value Euler's method gave at t=5.4?

Percentage error = ? percent
 
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well so what is euler's method? probably a good place start
 

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