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Description: |
This seminar is concerned with the approximate solution of forward-backward differential
equations of the general form x'(t)=α(t)x(t)+β(t)x(t-1)+γ(t)x(t+1).
We search for a solution x, defined for t∈[-1,k], (k∈N), which takes given
values on the intervals [-1,0] and (k-1,k]. We introduce and analyse some new computational
methods for the solution of this problem which are applicable both in the case of constant
and variable coefficients.
On the other hand, we transform the original equation in a (k-1)-th order ODE with boundary
conditions on the interval [0,1]. By analysing the obtained boundary value problem, we can
obtain existence results about the original problem and in the case where it is solvable,
we can obtain numerical solutions by applying standard computational methods for ODEs.
Numerical results are presented and compared with the results obtained by other methods.
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