Periodic, continuous and piecewise smooth function

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Discussion Overview

The discussion revolves around finding an initial condition function that is periodic, continuous, and piecewise smooth for numerical solutions to initial-boundary value problems in applied mathematics. Participants are exploring various function options to compare with the sine function in MATLAB simulations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant, ocean, is seeking suggestions for a function that meets the criteria of being periodic, continuous, and piecewise smooth.
  • Another participant suggests sin(x) as a suitable function, noting its properties.
  • Ocean expresses the need for alternative functions to compare with sin(x) in their numerical simulations.
  • A different participant proposes cos(x) as another option.
  • This participant also suggests a specific piecewise function defined as f(x) = x for 0 ≤ x ≤ 1, f(x) = 2 - x for 1 ≤ x ≤ 2, and continued periodically with a period of 1, questioning ocean's understanding of the function's properties.

Areas of Agreement / Disagreement

Participants have differing views on the adequacy of the suggested functions, with ocean seeking more alternatives beyond sin(x) and cos(x). The discussion remains unresolved regarding the best function to use.

fractional
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Dear friends,

I am a new member of physics forums, so this is may new message.
Already thanks to you for your helps to my question. I research some
applied mathematician problem's numerical solutions. There are initial-boundary value problems. I need an initial condition function which must be a periodic, continuous and
piecewise smooth type. Please vaiting for your suggestions.

ocean
 
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sin(x) is a continuous smooth piecewise function.
 
thanks for your suggestion, but I apply sin(x) to my problem, I need any other one to compare my numerical MATLAB simulation results. ıf you give me any other function, I can use for comparison.
thanks for your help.
 
Cos(x) works.

You just want some continuous, periodic, piecewise function? Okay, what about f(x)= x if [itex]0\le x\le 1[/itex], 2- x if [itex]1\le x\le 2[/itex] and continued periodically with period 1?

My question is, do you really understand what "continous, periodic, piecewise function" means? If you do, then it should be easy to make up hundreds of examples.
 

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