Piecewise orthogonal collocation for computing periodic solutions of renewal equations

被引：0

作者：

Ando, Alessia ^{[1
,2
]}

Breda, Dimitri ^{[2
]}

机构：

[1] Gran Sasso Sci Inst, Area Math, Via Francesco Crispi 7, I-67100 Laquila, Italy

[2] Univ Udine, CDLab Computat Dynam Lab, Dept Math Comp Sci & Phys, Via Sci 206, I-33100 Udine, Italy

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2023年 / 49卷 / 06期

关键词：

Renewal equations; Periodic solutions; Boundary value problems; Piecewise orthogonal collocation; Finite element method; Population dynamics; BOUNDARY-VALUE-PROBLEMS; DIFFERENTIAL-EQUATIONS; INTEGRAL-EQUATION; APPROXIMATION;

D O I：

10.1007/s10444-023-10094-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally, we show some numerical experiments confirming the theoretical results and a couple of applications in view of bifurcation analysis.

引用

页数：30

共 50 条

[21] On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations
Liang, Hui
Brunner, Hermann
BIT NUMERICAL MATHEMATICS, 2016, 56 (04) : 1339 - 1367
[22] Periodic solutions of delay differential equations with piecewise continuous arguments
Wang, GQ
Yan, JR
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2004, 35 (11): : 1293 - 1304
[23] Periodic solutions of a generalized system of piecewise linear difference equations
Tikjha, Wirot
Lapierre, Evelina
Lenbury, Yongwimon
ADVANCES IN DIFFERENCE EQUATIONS, 2015, : 1 - 15
[24] Periodic solutions of a generalized system of piecewise linear difference equations
Wirot Tikjha
Evelina Lapierre
Yongwimon Lenbury
Advances in Difference Equations, 2015
[25] Numerical Solutions of Coupled Nonlinear Schrodinger Equations by Orthogonal Spline Collocation Method
Meng, Qing-Jiang
Yin, Li-Ping
Jin, Xiao-Qing
Qiao, Fang-Li
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2012, 12 (05) : 1392 - 1416
[26] PIECEWISE CONTINUOUS COLLOCATION FOR INTEGRAL-EQUATIONS
ATKINSON, K
GRAHAM, I
SLOAN, I
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (01) : 172 - 186
[27] An Orthogonal Collocation Method for Sobolev Equations
Lu, Xiaofei
Ma, Ning
PROCEEDINGS OF THE 2015 6TH INTERNATIONAL CONFERENCE ON MANUFACTURING SCIENCE AND ENGINEERING, 2016, 32 : 1501 - 1504
[28] PRECONDITIONED RICHARDSON AND MINIMAL RESIDUAL ITERATIVE METHODS FOR PIECEWISE HERMITE BICUBIC ORTHOGONAL SPLINE COLLOCATION EQUATIONS
BIALECKI, B
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1994, 15 (03): : 668 - 680
[29] Pseudo almost periodic solutions of differential equations with piecewise constant argument
Piao, DX
Yuan, R
CHINESE ANNALS OF MATHEMATICS SERIES B, 1999, 20 (04) : 489 - 494
[30] Periodic solutions of differential equations with a general piecewise constant argument and applications
Chiu, Kuo-Shou
Pinto, Manuel
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2010, (46) : 1 - 19

← 1 2 3 4 5 →