Homotopy Analysis Method for Stochastic Differential Equations with Maxima

被引：0

作者：

Janowicz, Maciej ^{[1
,2
]}

Kaleta, Joanna ^{[1
]}

Krzyzewski, Filip ^{[2
]}

Rusek, Marian ^{[1
]}

Orlowski, Arkadiusz ^{[1
]}

机构：

[1] Warsaw Univ Life Sci SGGW, Fac Appl Informat & Math WZIM, PL-02775 Warsaw, Poland

[2] Polish Acad Sci, Inst Phys, PL-02668 Warsaw, Poland

来源：

COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING (CASC 2015) | 2015年 / 9301卷

关键词：

homotopy analysis method; stochastic differential equations; quantum scalar field; computer algebra systems; Maxima; ASYMPTOTIC METHOD; FLOW;

D O I：

10.1007/978-3-319-24021-3_18

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The homotopy analysis method known from its successful applications to obtain quasi-analytical approximations of solutions of ordinary and partial differential equations is applied to stochastic differential equations with Gaussian stochastic forces. It has been found that the homotopy analysis method yields excellent agreement with exact results (when the latter are available) and appears to be a very promising approach in the calculations related to quantum field theory and quantum statistical mechanics. Using a computer algebra system Maxima has considerably influnced and simplified the calculations and results.

引用

页码：233 / 244

页数：12

共 21 条

[1]

[Anonymous], T VVIA

[2]

[Anonymous], LECT NOTES PHYS

[3] STRONG COUPLING EXPANSION FOR CLASSICAL STATISTICAL DYNAMICS [J].

BENDER, CM ;

COOPER, F ;

GURALNIK, G ;

ROSE, HA ;

SHARP, DH .

JOURNAL OF STATISTICAL PHYSICS, 1980, 22 (06) :647-660

[4] EQUIVALENT LINEARIZATION TECHNIQUES [J].

CAUGHEY, TK .

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1963, 35 (11) :1706-+

[5] STOCHASTIC QUANTIZATION [J].

DAMGAARD, PH ;

HUFFEL, H .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1987, 152 (5-6) :227-+

[6] Applicability of the linear δ expansion for the λφ4 field theory at finite temperature in the symmetric and broken phases [J].

Farias, R. L. S. ;

Krein, G. ;

Ramos, Rudnei O. .

PHYSICAL REVIEW D, 2008, 78 (06)

[7] LANGEVIN SIMULATION IN MINKOWSKI SPACE [J].

GOZZI, E .

PHYSICS LETTERS B, 1985, 150 (1-3) :119-124

[8] STOCHASTIC QUANTIZATION IN MINKOWSKI SPACE [J].

HUFFEL, H ;

RUMPF, H .

PHYSICS LETTERS B, 1984, 148 (1-3) :104-110

[9]

Kevorkian J., 1996, Multiple Scale and Singular Perturbation Methods. Applied Mathematical Sciences, DOI [DOI 10.1007/978-1-4612-3968-0, 10.1007/978-1-4612-3968-0]

[10] A general approach to obtain series solutions of nonlinear differential equations [J].

Liao, S. ;

Tan, Y. .

STUDIES IN APPLIED MATHEMATICS, 2007, 119 (04) :297-354

← 1 2 3 →