An algorithm for the numerical solution of the multivariate master equation for stochastic coalescence

Alfonso, L.

doi:https://doi.org/10.5194/acp-15-12315-2015

Articles | Volume 15, issue 21

https://doi.org/10.5194/acp-15-12315-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/acp-15-12315-2015

© Author(s) 2015. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 15, issue 21

Research article

|

06 Nov 2015

Research article |

| 06 Nov 2015

An algorithm for the numerical solution of the multivariate master equation for stochastic coalescence

L. Alfonso

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HTML: 1,361
PDF: 821
XML: 188
Total: 2,370
BibTeX: 99
EndNote: 80

Views and downloads (calculated since 23 Apr 2015)

Month	HTML	PDF	XML	Total
Apr 2015	48	48	2	98
May 2015	33	28	1	62
Jun 2015	14	15	3	32
Jul 2015	15	9	3	27
Aug 2015	5	2	4	11
Sep 2015	10	7	2	19
Oct 2015	6	4	2	12
Nov 2015	133	95	14	242
Dec 2015	19	45	10	74
Jan 2016	42	18	6	66
Feb 2016	22	9	2	33
Mar 2016	20	8	2	30
Apr 2016	5	7	0	12
May 2016	11	8	0	19
Jun 2016	6	4	1	11
Jul 2016	10	6	3	19
Aug 2016	8	5	0	13
Sep 2016	9	1	10
Oct 2016	13	9	1	23
Nov 2016	8	4	0	12
Dec 2016	3	1	0	4
Jan 2017	11	2	0	13
Feb 2017	11	2	1	14
Mar 2017	14	10	1	25
Apr 2017	14	9	0	23
May 2017	24	12	2	38
Jun 2017	25	3	2	30
Jul 2017	17	2	0	19
Aug 2017	10	6	3	19
Sep 2017	7	9	3	19
Oct 2017	5	6	2	13
Nov 2017	8	7	0	15
Dec 2017	4	3	0	7
Jan 2018	6	4	1	11
Feb 2018	2	4	0	6
Mar 2018	7	9	0	16
Apr 2018	6	3	3	12
May 2018	8	6	1	15
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Jul 2018	4	5	1	10
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Sep 2018	7	8	1	16
Oct 2018	7	7	1	15
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Dec 2018	7	6	3	16
Jan 2019	5	9	1	15
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Nov 2019	3	3	0	6
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Jan 2020	6	4	0	10
Feb 2020	3	3	0	6
Mar 2020	3	5	3	11
Apr 2020	2	3	0	5
May 2020	6	7	0	13
Jun 2020	19	4	3	26
Jul 2020	10	9	6	25
Aug 2020	5	8	2	15
Sep 2020	6	3	3	12
Oct 2020	6	1	0	7
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Dec 2020	7	2	5	14
Jan 2021	13	10	5	28
Feb 2021	8	3	7	18
Mar 2021	8	7	5	20
Apr 2021	5	6	3	14
May 2021	6	8	2	16
Jun 2021	4	1	2	7
Jul 2021	4	0	4
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Jan 2023	5	6	0	11
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Apr 2023	1	3	0	4
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Jun 2023	35	6	2	43
Jul 2023	34	5	1	40
Aug 2023	36	9	2	47
Sep 2023	35	2	1	38
Oct 2023	35	4	1	40
Nov 2023	23	1	0	24
Dec 2023	36	3	2	41
Jan 2024	36	2	0	38
Feb 2024	30	3	0	33
Mar 2024	36	8	3	47
Apr 2024	18	3	2	23

Cumulative views and downloads (calculated since 23 Apr 2015)

Month	HTML	PDF	XML	Total
Apr 2015	48	48	2	98
May 2015	33	28	1	62
Jun 2015	14	15	3	32
Jul 2015	15	9	3	27
Aug 2015	5	2	4	11
Sep 2015	10	7	2	19
Oct 2015	6	4	2	12
Nov 2015	133	95	14	242
Dec 2015	19	45	10	74
Jan 2016	42	18	6	66
Feb 2016	22	9	2	33
Mar 2016	20	8	2	30
Apr 2016	5	7	0	12
May 2016	11	8	0	19
Jun 2016	6	4	1	11
Jul 2016	10	6	3	19
Aug 2016	8	5	0	13
Sep 2016	9	1	10
Oct 2016	13	9	1	23
Nov 2016	8	4	0	12
Dec 2016	3	1	0	4
Jan 2017	11	2	0	13
Feb 2017	11	2	1	14
Mar 2017	14	10	1	25
Apr 2017	14	9	0	23
May 2017	24	12	2	38
Jun 2017	25	3	2	30
Jul 2017	17	2	0	19
Aug 2017	10	6	3	19
Sep 2017	7	9	3	19
Oct 2017	5	6	2	13
Nov 2017	8	7	0	15
Dec 2017	4	3	0	7
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Feb 2018	2	4	0	6
Mar 2018	7	9	0	16
Apr 2018	6	3	3	12
May 2018	8	6	1	15
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Aug 2021	2	6	2	10
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Oct 2021	7	38	4	49
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Feb 2022	5	8	1	14
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Apr 2022	4	5	1	10
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Jan 2023	5	6	0	11
Feb 2023	5	5	0	10
Mar 2023	24	1	1	26
Apr 2023	1	3	0	4
May 2023	25	7	0	32
Jun 2023	35	6	2	43
Jul 2023	34	5	1	40
Aug 2023	36	9	2	47
Sep 2023	35	2	1	38
Oct 2023	35	4	1	40
Nov 2023	23	1	0	24
Dec 2023	36	3	2	41
Jan 2024	36	2	0	38
Feb 2024	30	3	0	33
Mar 2024	36	8	3	47
Apr 2024	18	3	2	23

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Latest update: 15 Apr 2024

Short summary

The mathematical description of finite volume coalescing systems relies on the multivariate master equation. However, due to its complexity, it has analytical solutions only for a limited number of kernels and initial conditions. In this paper, in an effort to solve this problem, we have introduced a novel numerical approach to calculate the solution of the multivariate coalescence master equation that works for any type of kernel and initial conditions.

An algorithm for the numerical solution of the multivariate master equation for stochastic coalescence

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Cited

7 citations as recorded by crossref.

6 citations as recorded by crossref.

1 citations as recorded by crossref.

Saved (final revised paper)