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Sina
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Specifying history for delay differential equations ``near infinity'' (using NDSolve)

Consider the following simple DDE:

$ f''(x)+ f(x+1) = 0.$$ f''(x)+ f(x+ 1) = 0.$

For $ x \gg 1$, this DDE reducesshould approximately reduce to that of a simple harmonic oscillator: $f''(x)+f(x) \approx 0$. Suppose that for some physical reason I require $f(x) = \sin{x}$ for large $x$ and then use this as a ``history'' for the above DDE. I am then interested to see what $f(x)$ is in the vicinity of $x=0$.

The problem is that (not surprisingly) depending on where I set the history condition (when using NDSolve), I will get a different answer for $f(x)$ near $x=0$. Any suggestions for how to properly handle this?

Specifying history for delay differential equations ``near infinity''

Consider the following simple DDE:

$ f''(x)+ f(x+1) = 0.$

For $ x \gg 1$, this DDE reduces to that of a simple harmonic oscillator: $f''(x)+f(x) \approx 0$. Suppose that for some physical reason I require $f(x) = \sin{x}$ for large $x$ and then use this as a ``history'' for the above DDE. I am then interested to see what $f(x)$ is in the vicinity of $x=0$.

The problem is that (not surprisingly) depending on where I set the history condition I will get a different answer for $f(x)$ near $x=0$. Any suggestions for how to properly handle this?

Specifying history for delay differential equations ``near infinity'' (using NDSolve)

Consider the following DDE:

$ f''(x)+ f(x+ 1) = 0.$

For $ x \gg 1$, this DDE should approximately reduce to that of a simple harmonic oscillator: $f''(x)+f(x) \approx 0$. Suppose that for some physical reason I require $f(x) = \sin{x}$ for large $x$ and then use this as a ``history'' for the above DDE. I am then interested to see what $f(x)$ is in the vicinity of $x=0$.

The problem is that (not surprisingly) depending on where I set the history condition (when using NDSolve), I get a different answer for $f(x)$ near $x=0$. Any suggestions for how to properly handle this?

Source Link
Sina
Sina
  • 101
  • 1
  • 3

Specifying history for delay differential equations ``near infinity''

Consider the following simple DDE:

$ f''(x)+ f(x+1) = 0.$

For $ x \gg 1$, this DDE reduces to that of a simple harmonic oscillator: $f''(x)+f(x) \approx 0$. Suppose that for some physical reason I require $f(x) = \sin{x}$ for large $x$ and then use this as a ``history'' for the above DDE. I am then interested to see what $f(x)$ is in the vicinity of $x=0$.

The problem is that (not surprisingly) depending on where I set the history condition I will get a different answer for $f(x)$ near $x=0$. Any suggestions for how to properly handle this?