数学代写|Ordinary Differential Equation, Error Analysis and Accuracy Improvement
AUTHOR
essaygo
PUBLISHED ON:
2022年10月24日
PUBLISHED IN:

这是一篇来自美国的关于常微分方程、误差分析及精度改进的数学代写

 

Assignment

Consider a numerical analysis of a differential equation,

y ′′ = y, (1)

with initial conditions for:

y = 0 and y= 1 at x = 0

The exact solution is known to be

y = sin x.

Conduct numerical analysis for 0 x 2π using various methods and analyze the following items:

  • errors in amplitude A (= √y2 + y2) and phase ϕ (= tan1(y/y)) at x = 2π.
  • accuracy improvement by Richardson extrapolation and/or introducing higher-order methods.
  • discuss on stability of the methods.
  • work load, coding efforts, etc.

The report should be in A4 size and include a description of the problem, methods, analysis with fifigures and tables, discussion, and conclusions. MATLAB code written in live-script (.mlx) should be presented as an appendix.

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