Question

# How to use finite difference method while required information for solving is not available???

Hi
I'm solving nonlinear second order equation by using finite difference method . finally for calculating value at any desired node, knowing three preceding nodes is required however by knowing boundary condition just one of these nodes becomes obvious and still knowing two other values is necessary. it must be noted there are plenty of guesses for values of these nodes which lead to compatible response.

National Mining University of Ukraine
Напишите уравнение и граничные условия. Тогда я смогу Вам помочь...

## Top contributors to discussions in this field

Anton Vrdoljak
University of Mostar
In the case of ODE, this website offer a nice explanation:
Panchatcharam Mariappan
Indian Institute of Technology Tirupati
it would be best if you used a combination of the Newton-Raphson and finite difference methods as your equation is nonlinear.
Filippo Maria Denaro
Università degli Studi della Campania "Luigi Vanvitelli
Could you address the full equation and conditions?
Alireza Akbari
Khaje Nasir Toosi University of Technology
thanks for sharing this useful article.
Alireza Akbari
Khaje Nasir Toosi University of Technology
Dear panchatcharam, As I know Newton-Raphson method is a way to quickly find a good approximation for the root of a real-valued function f(x)=0. Im wondering how this method can help me to find boundary conditions. could you explain more please.
Alireza Akbari
Khaje Nasir Toosi University of Technology
Dear Filippo, the equation is in following attached file. it must be noted C1,C2 and C3 are constants.
Filippo Maria Denaro
Università degli Studi della Campania "Luigi Vanvitelli
please write the ODE, not only the discretization You used.
Your discretization needs of a linearization to be recasted in a tri-diagonal like system. You have a boundary value ODE and the condition at N must enter in a different way from an initial boundary value problem.
however, in generale, for multi-step methods you need to create the starting values using a single-step method for all required nodes. Use a discretization of the same accuracy.
Note that the second order ODE could be written as system of two first order ODE.
1 Recommendation
Anton Vrdoljak
University of Mostar
You're welcome Alireza Akbari.
Alireza Akbari
Khaje Nasir Toosi University of Technology
I attached simple form of ode.
Filippo Maria Denaro
Università degli Studi della Campania "Luigi Vanvitelli
You can cast the form of a non-linear algebric system A(Y).Y=q and use some Classic solver for such problems.
National Mining University of Ukraine
Напишите уравнение и граничные условия. Тогда я смогу Вам помочь...

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