National Mining University of Ukraine
Question
Asked 19th Jun, 2022
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.
Most recent answer
Напишите уравнение и граничные условия. Тогда я смогу Вам помочь...
All Answers (11)
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.
Università degli Studi della Campania "Luigi Vanvitelli
Could you address the full equation and conditions?
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.
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.

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
University of Mostar
You're welcome Alireza Akbari.
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.
Similar questions and discussions
What are the steps to query data for machine learning from Materials project using API?
Ankur Taya
I have tried the following steps, but these are giving the errors
1. !pip install pymatgen
2. !pip install mp_api
2. from mp_api.client import MPRester
with MPRester("my_api_key") as mpr:
docs = mpr.summary.search(material_ids=["mp-149", "mp-13", "mp-22526"])
And got a very long error as a result.
What am I doing wrong?
Related Publications
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions (symmetric and non-symmetric) are studied in this work. Reliability of results obtained is verified by the finite difference method (FDM) with spatial approximation of () 2 O c and the finite element method (FEM) with the...
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions
(symmetric and non-symmetric) are studied in this work. Reliability of the obtained results is verified by the finite difference
method (FDM) and the finite element method (FEM) with the Bubnov-Galerkin approximation for v...
This work presents a methodology for the use of finite differences in two-dimensional eigenproblems using a mesh of triangles produced for the finite dement method. Expressions are given for the first and second derivatives at a grid point in terms of nodal values at neighboring points. The method has been tested analysing a waveguide resonator inc...