[rst1993]

while solving a diffusion problem using second order accurate finite difference scheme in computational domain, error from using first order accurate Neumann boundary condition is less than from second order accurate newmann boundary condition. is this possible or am i doing it wrong?

[virendra_p]

Can you describe your problem in detail?

[rst1993]

d^2u/dx^2=-10 sin(pi*x/50)
with one side dirchelet and another side neumann bc

[virendra_p]

Here's something that might help .. http://www.scientificpython.net/pybl...different-ways ..meanwhile i'll try solving it just to recheck...good luck!

[adrin]

Incidentally, if one uses a finite volume formulation, instead of finite difference, one will _automatically_ end up with method 3 described in the link

Adrin

[FMDenaro]

Originally Posted by rst1993

while solving a diffusion problem using second order accurate finite difference scheme in computational domain, error from using first order accurate Neumann boundary condition is less than from second order accurate newmann boundary condition. is this possible or am i doing it wrong?

how do you discretize the Neumann bc ?

[rst1993]

Originally Posted by FMDenaro

how do you discretize the Neumann bc ?

first i used a first order accurate finite difference and in another case using 2nd order accurate finite difference scheme.

[FMDenaro]

Originally Posted by rst1993

first i used a first order accurate finite difference and in another case using 2nd order accurate finite difference scheme.

I mean how do you implement both formula on the boundry

[virendra_p]

Backward diff. for 1st order and central diff. for second order...

[FMDenaro]

ok, suppose to work in the 1D problem f'' = q. I think you have some like a Neumann + Dirchlet BC.s, for example f'(x0)=p, f(L)=fL.

Consider i=1 the node at x0. Therefore,

(f(1)-2f(2)+f(3))/h^2 = q(2)

is the FD equation that requires Neumann BC.

1) first order

(f(2)-f(1))/h=p(1) -> f(1)=f(2)- h* p(1) .... OK!

2) second order central

(f(2)-f(0))/2*h = p(1)

and you see that the node 1 is not expressed and you have no way to substitute into the equation.

Please clarify your procedure ....

[virendra_p]

Second order discretization will require additional condition to eliminate the unknown...check: http://www.scientificpython.net/pybl...different-ways

[FMDenaro]

Originally Posted by virendra_p

Second order discretization will require additional condition to eliminate the unknown...check: http://www.scientificpython.net/pybl...different-ways

For that, I strongly suggest to use a second order backward discretization that automatically provides the value at node 1 expressed in terms of node 2,3 and value of the derivative at 1. It is simple and more accurate than other

[rst1993]

Originally Posted by FMDenaro

ok, suppose to work in the 1D problem f'' = q. I think you have some like a Neumann + Dirchlet BC.s, for example f'(x0)=p, f(L)=fL.

Consider i=1 the node at x0. Therefore,

(f(1)-2f(2)+f(3))/h^2 = q(2)

is the FD equation that requires Neumann BC.

1) first order

(f(2)-f(1))/h=p(1) -> f(1)=f(2)- h* p(1) .... OK!

2) second order central

(f(2)-f(0))/2*h = p(1)

and you see that the node 1 is not expressed and you have no way to substitute into the equation.

Please clarify your procedure ....

for 1st order accurate at boundary i used a backward difference (u(i)-u(i-1))/dx and for 2nd order accurate i used a backward biased finite difference (3u(i)-4u(i-1)+u(i-2))/2dxfor neumann bc.
in the main computational domain i used a central difference scheme.

[FMDenaro]

Originally Posted by rst1993

for 1st order accurate at boundary i used a backward difference (u(i)-u(i-1))/dx and for 2nd order accurate i used a backward biased finite difference (3u(i)-4u(i-1)+u(i-2))/2dxfor neumann bc.
in the main computational domain i used a central difference scheme.

ok, that's must definitely work fine ...could you show the convergence curves for both shcemes?