Convergence results for unbounded solutions of first order non-linear differential-functional equations

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Institute of Mathematics, University of Gdańsk, 57 Wita Stwosza St., 80-952 Gdańsk, Poland

We consider the Cauchy problem in an unbounded region for equations of the type either

D_{t} z (t, x) = f (t, x, z (t, x), z_{(t, x)}, D_{x} z (t, x))

or

D_{t} z (t, x) = f (t, x, z (t, x), z, D_{x} z (t, x))

. We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.

error estimates, recurrence inequalities, difference scheme

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