Solving Airy's Equation: Numerical Method & Steps

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SUMMARY

This discussion focuses on numerically solving Airy's equation, specifically y''=xy, on the interval 0 PREREQUISITES

  • Understanding of differential equations, specifically second-order linear equations.
  • Familiarity with numerical methods for solving differential equations.
  • Knowledge of power series and their convergence properties.
  • Basic skills in mathematical notation and manipulation, particularly summation notation.
NEXT STEPS
  • Study numerical methods for solving differential equations, focusing on finite difference methods.
  • Learn about power series solutions and their applications in differential equations.
  • Explore software tools like MATLAB or Python's SciPy for numerical simulations of differential equations.
  • Investigate the convergence criteria for power series to ensure valid solutions.
USEFUL FOR

Mathematicians, physicists, and engineers involved in solving differential equations, particularly those interested in numerical methods and power series solutions.

robbin53
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Numerically solve for the solution of Airy's equation y''=xy on the interval 0<x<1 with boundary conditions y(0)=y'(0)=1. Use the trial solution

yhat = 1 + x + (sumation j = 2 through N) csubj*x^j.

Where do I get started? I am so lost.
 
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hmm I can't really understand the sumattion you posted, but normally you would assume that the solution takes the form of an infinite power series.

then you plug in for y and y' and simplify.
 
Thanks, I started that to do that, I'm glad I'm going about it the right way!
 

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