Modified Patankar Linear Multistep Methods for Production-Destruction Systems

被引：1

作者：

Izzo, Giuseppe ^{[1
,3
]}

Messina, Eleonora ^{[1
,3
]}

Pezzella, Mario ^{[2
,3
]}

Vecchio, Antonia ^{[2
,3
]}

机构：

[1] Univ Naples Federico II, Dept Math & Applicat, Via Cintia, I-80126 Naples, Italy

[2] CNR Natl Res Council Italy, Inst Appl Computat Mauro Picone, Via P Castellino 111, I-80131 Naples, Italy

[3] INdAM Res Grp GNCS, Rome, Italy

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2025年 / 102卷 / 03期

关键词：

Patankar-type schemes; Positivity-preserving; High order; Conservativity; Linear multistep methods; LIFE-CYCLE; HIGH-ORDER; POSITIVITY; MODEL; DISCRETIZATIONS; EQUATIONS; DYNAMICS; SCHEMES;

D O I：

10.1007/s10915-025-02804-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weights denominators to achieve it.

引用

页数：39

共 47 条

[1] THE DYNAMICS OF PRODUCTION AND DESTRUCTION - ANALYTIC INSIGHT INTO COMPLEX BEHAVIOR [J].