National Mining University of Ukraine
Asked 19th Jun, 2022
How to use finite difference method while required information for solving is not available???
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.
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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.
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