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Topological Solution of Ordinary and Partial Finite Difference Equations

Adel F. Antippa and Nguyen K. Toan
Journal of Mathematical Physics
vol. 21, no. 10, pp. 2475-2480 (1980)

Using the discrete path formalism, we obtain a topological solution for ordinary, as well as partial, linear inhomogeneous finite difference equations with variable coefficients and arbitrarily specified boundary conditions. The solution is homomorphic to a set of discrete paths constructed from a set of vectors determined by the level differences of the equation.

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