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- W2100989435 abstract "The paper deals with the Darboux problem for the equa- tion Dxyz(x;y) = f(x;y;z(x;y)) where z(x;y) is a function deÞned by z(x;y)(t;s) = z(x + t;y + s), (t;s) 2 (Aa0;0) C (Ab0;0). We construct a general class of dierence methods for this problem. We prove the existence and uniqueness of solutions to implicit functional dierence equations by means of a comparison method; moreover we give an er- ror estimate. The convergence of explicit dierence schemes is proved under a general assumption that given functions satisfy nonlinear es- timates of the Perron type. Our results are illustrated by a numerical example." @default.
- W2100989435 created "2016-06-24" @default.
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- W2100989435 date "1998-01-01" @default.
- W2100989435 modified "2023-09-26" @default.
- W2100989435 title "Numerical Solutions to the Darboux Problem with Functional Dependence" @default.
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- W2100989435 doi "https://doi.org/10.1023/b:geor.0000008139.17048.bf" @default.
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