Re: ODE to difference equation and solution
- From: A.L. <alewando@xxxxxxxxxxxx>
- Date: Fri, 19 Jan 2007 07:58:29 -0600
On Thu, 18 Jan 2007 23:05:44 GMT, "Calvin Guan"
<hguan@xxxxxxxxxxxxxxxxxxx> wrote:
Hello,
I'm trying to convert an 2nd order ODE to difference equation and solve it
numerically. Here is an example.
y''=sin(x), given the IC y(0)=0 and BC y(3.14)=0. This can be solved
analytically if y'(0) is known.
I convert the ODE to DE like:
y(n+1)-2y(n)+y(n-1)=h*h*sin(n*h)
given initial value y(0)=0
and final y(m+1)=0 where h=3.14/(m+1)
This can be solved by constructing a m*m matrix. but it became very resource
demanding if m is big. I try to solve it by z-transform but I don't have the
value for y(1).
How this can be solved efficiently?
By solving numerically equation for y'(0).
See the book: "Quasilinearization and nonlinear boundary-value
problems" (Modern analytic and computational methods in science and
mathematics) by Richard Ernest Bellman
A.L.
.
- References:
- ODE to difference equation and solution
- From: Calvin Guan
- ODE to difference equation and solution
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