Mean square convergent numerical methods for nonlinear random differential equations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5890 LNCS, Issue , 2010, Pages 1-21

  Cortes J C ^a   Jodar L ^a   Villanueva, R J ^a   Villafuerte, L ^b  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE CHIAPAS   (Mexico)

Author keywords

Mean square calculus; Numerical solution; Random differential equation

Indexed keywords

EULER SCHEME; ILLUSTRATIVE EXAMPLES; MEAN SQUARE; NUMERICAL SOLUTION; RANDOM DIFFERENTIAL EQUATIONS; RANDOM MATRIX; STOCHASTIC APPROXIMATIONS;

APPROXIMATION THEORY; CALCULATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); INITIAL VALUE PROBLEMS; NUMERICAL ANALYSIS; NUMERICAL METHODS;

NONLINEAR EQUATIONS;

EID: 77952000054     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-11389-5_1     Document Type: Conference Paper

References (15)

1. Barron, R., Ayala, G.: El método de yuxtaposición de dominios en la solución numérica de ecuaciones diferenciales estocásticas. In: Proc. Metodos Numéricos en Ingeniería y Ciencias Aplicadas (CIMNE), Monterrey, Mexico, pp. 267-276 (2002)
2. Braumann, C.A.: Variable effort harvesting models in random environments: generalization to density-dependent noise intensities. Math. Biosci. 177-178, 229-245 (2002)
3. Chilès, J., Delfiner, P.: Geostatistics. Modelling Spatial Uncertainty. John Wiley, New York (1999)
4. Dieudonnè, J.: Foundations of Modern Analysis. Academic Press, New York (1960)
5. El-Tawil, M.A.: The approximate solutions of some stochastic differential equations using transformations. Applied Mathematics and Computation 164(1), 167-178 (2005)
6. Golub, G., Van Loan, C.F.: Matrix Computations. The Johns Hopkins University Press, Baltimore (1989)
7. Grüne, L., Kloeden, P.E.: Pathwise approximation of random ordinary differential equations. BIT 41(4), 711-721 (2001) (Pubitemid 33631362)
8. Henrici, P.: Discrete Variable Methods in Ordinary Differential Equations. John Wiley and Sons, New York (1962)
9. Jódar, L., Cortés, J.C., Villafuerte, L.: A discrete eigenfunctions method for numerical solution of random diffusion models. In: Conf. Differential and Difference Equations and Applications, Miami, vol. 13, pp. 457-466. Hindawi Publ. Corp., Miami (2006)
10. Keller, J.B.: Wave propagation in random media. In: Proc. Symp. Appl. Math., vol. 13, pp. 227-246. Amer. Math. Soc., Providence (1962)
11. Keller, J.B.: Stochastic equations and wave propagation in random media. In: Proc. Symp. Appl. Math., New York, vol. 16, pp. 145-170. Amer. Math. Soc., Providence (1964)
12. Ross, S.M.: Simulation. Academic Press, New York (2002)
13. Soong, T.T.: Random Differential Equations in Science and Engeneering. Academic Press, New York (1973)
14. Strand, J.L.: Random ordinary differential equations. J. Differential Equations 7, 538-553 (1973)
15. Talay, D.: Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastics Analysis and Applications 8(4), 483-509 (1990)