Numerical method for ODEs without frequency error
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To solve an ODE numerically,
one usually use finite difference methods.
For example,
simple harmonic oscillator, i.e.
$$y''=-omega^2y$$
can be discretized by
$$frac{y_{n+1}-2y_n+y_{n-1}}{Delta x^2}=-omega^2y_n$$
However, if we use this formula to solve the equation,
the frequency of the numerical solution is different from
true frequency $omega$.
Then my question is,
is there any discretization method without frequency error?
For example, is Runge-Kutta method similarly suffer from frequency error?
EDIT
Simple harmonic oscillator is just an example.
My equation is actually PDE (Wave equation).
numerical-methods finite-differences finite-difference-methods
asked yesterday
Shu S
183
add a comment |
up vote
0
down vote
favorite
To solve an ODE numerically,
one usually use finite difference methods.
For example,
simple harmonic oscillator, i.e.
$$y''=-omega^2y$$
can be discretized by
$$frac{y_{n+1}-2y_n+y_{n-1}}{Delta x^2}=-omega^2y_n$$
However, if we use this formula to solve the equation,
the frequency of the numerical solution is different from
true frequency $omega$.
Then my question is,
is there any discretization method without frequency error?
For example, is Runge-Kutta method similarly suffer from frequency error?
EDIT
Simple harmonic oscillator is just an example.
My equation is actually PDE (Wave equation).
numerical-methods finite-differences finite-difference-methods
asked yesterday
Shu S
183
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
To solve an ODE numerically,
one usually use finite difference methods.
For example,
simple harmonic oscillator, i.e.
$$y''=-omega^2y$$
can be discretized by
$$frac{y_{n+1}-2y_n+y_{n-1}}{Delta x^2}=-omega^2y_n$$
However, if we use this formula to solve the equation,
the frequency of the numerical solution is different from
true frequency $omega$.
Then my question is,
is there any discretization method without frequency error?
For example, is Runge-Kutta method similarly suffer from frequency error?
EDIT
Simple harmonic oscillator is just an example.
My equation is actually PDE (Wave equation).
numerical-methods finite-differences finite-difference-methods
asked yesterday
Shu S
183
To solve an ODE numerically,
one usually use finite difference methods.
For example,
simple harmonic oscillator, i.e.
$$y''=-omega^2y$$
can be discretized by
$$frac{y_{n+1}-2y_n+y_{n-1}}{Delta x^2}=-omega^2y_n$$
However, if we use this formula to solve the equation,
the frequency of the numerical solution is different from
true frequency $omega$.
Then my question is,
is there any discretization method without frequency error?
For example, is Runge-Kutta method similarly suffer from frequency error?
EDIT
Simple harmonic oscillator is just an example.
My equation is actually PDE (Wave equation).
numerical-methods finite-differences finite-difference-methods
numerical-methods finite-differences finite-difference-methods
asked yesterday
Shu S
183
asked yesterday
Shu S
183
edited yesterday
asked yesterday
Shu S
183
asked yesterday
Shu S
183
asked yesterday
Shu S
183
183
add a comment |
add a comment |
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