CONTENTS Introduction......................................................................................................................................... 5 § 1. A maximum principle for linear mappings.................................................................................... 6 § 2. A maximum principle for nonlinear mappings............................................................................. 9 § 3. A finite difference analogue of a maximum principle for nonlinear elliptic equations.......... 11 § 4. A finite difference scheme of higher order accuracy.................................................................... 16 § 5. A maximum principle for systems of ordinary differential equations....................................... 23 § 6. The method of lines for nonlinear parabolic equations which can be degenerated to elliptic equations.................................................................................................................................... 27 §7. A geometrical interpretation of a maximum principle for a system of difference equations..................................................................................................................................................... 30 §8. A strong maximum principle for an elliptic system of nonlinear equations............................. 33 References.................................................................................................................................................. 41
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