Fundamental solutions of partial difference equations

Veit J.

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Fundamental solutions of partial difference equations

机译：偏差分方程的基本解

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In this paper a general integral formula for the fundamental solution of a linear partial difference equation with constant coefficients is investigated. For equations in twodimensional space, especially for the discretization of the Helmholtz equation, special integral formulae are given and the convergence of corresponding integrals is proved. The limits of the fundamental solution at infinity are calculated in several cases. [References: 5]

机译：本文研究了一个常系数线性偏差分方程基本解的一般积分公式。对于二维空间中的方程，特别是对于亥姆霍兹方程的离散化，给出了特殊的积分公式，并证明了相应积分的收敛性。在几种情况下，可以计算出无穷大时基本解的极限。 [参考：5]

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2003年第1期|共9页
作者
Veit J.;
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正文语种 eng
中图分类应用数学;
关键词
Partial difference equation; Difference equations in several variables; Fundamental solution; Integral representation; Discretized helmholtz equation; Limit at infinity;

机译：偏差分方程;几个变量的差分方程;基本解;积分表示;离散亥姆霍兹方程;无穷大;

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专利

1. Fundamental solutions of partial difference equations [J] . Veit J. Zeitschrift fur Angewandte Mathematik und Mechanik . 2003,第1期

机译：偏差分方程的基本解
2. Variations on the Fundamental Principle for Linear Systems of Partial Differential and Difference Equations with Constant Coefficients [J] . Ulrich Oberst Applicable algebra in engineering, communication and computing . 1995,第4a5期

机译：常系数偏微分和差分方程线性系统基本原理的变化
3. Solutions of Complex Fermat-Type Partial Difference and Differential-Difference Equations (vol 15, 227, 2018) [J] . Mediterranean journal of mathematics . 2020,第1期

机译：复杂的Fermat型偏差和差分方程的解（Vol 15,227,2018）
4. The Similarity Finite Difference Solutions for Two-Dimensional Parabolic Partial Differential Equations via SOR Iteration [C] . N. A. M. Ali, J. Sulaiman, A. Saudi, International Conference on Computational Science and Technology . 2020

机译：通过SOR迭代的二维抛物线局部微分方程的相似性有限差分解
5. Twin solutions of even order boundary value problems for ordinary differential equations and finite difference equations. [D] . Sun, Xun. 2009

机译：常微分方程和有限差分方程偶数边值问题的孪生解。
6. High accuracy finite difference approximation to solutions of elliptic partial differential equations [O] . Robert E. Lynch, John R. Rice 1978

机译：椭圆型偏微分方程解的高精度有限差分近似
7. On the Fundamental Solutions of Linear Fuchsian Partial Differential Equations (Hyperbolic Equations and Irregularities) [O] . Saito Toshiaki 2003

机译：关于线性Fuchsian偏微分方程（双曲型方程和不规则性）的基本解
8. APPLICATION OF THE THEORY OF HORMANDER TO FINDING THE FUNDAMENTAL SOLUTION OF HYPERBOLIC LINEAR PARTIAL DIFFERENTIAL EQUATIONS [R] . F. Edward Ehlers 1965

机译：应用HORmaNDER理论求解双曲型线性偏微分方程的基本解

Fundamental solutions of partial difference equations

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