## A discrete maximum principle |

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### Contents

Introduction | 5 |

A maximum principle for linear mappings | 6 |

A maximum principle for nonlinear mappings | 9 |

Copyright | |

7 other sections not shown

### Common terms and phrases

approximation attains its maximum boundary dQh boundary value problem connected net Q consider the following Corollary 1.2 defined Definition 1.3 denotes diagonal difference analogue difference equations difference scheme 4.3 differential equations discrete maximum principle DISSERTATIONES MATHEMATICAE dxtdxk ends the proof equations of form finite difference methods finite difference scheme following inequality following system iheQh inverse matrix Let Q Let us consider lexicographical ordering matrix A belongs matrix M(v method of lines monotone nonlinear elliptic equations obtain the following operator of positive ordinary differential equations point jh positive type principle for nonlinear priori estimation Ps)fe R. S. Varga RN spanned satisfies a maximum satisfies the assumptions satisfies the following satisfies the inequality satisfies the maximum set Q Smax Sniadeckich space RN strong maximum principle system of equations Theorem unit matrix unit vector v(ih v(tp Varga's maximum principle VN(C weak connected