A Lattice Scheme for Stochastic Partial Differential Equations of Elliptic Type in Dimension d {>=} 4

Journal Article · Wed Nov 15 00:00:00 EST 2006 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-006-0874-1· OSTI ID:21064200

Martinez, Teresa ^[1]; Sanz-Sole, Marta ^[2]

---

1. Departamento de Matematicas, Universidad Autonoma de Madrid, Campus de Cantoblanco, E-28049 (Spain)
2. Facultat de Matematiques, Universitat de Barcelona, Gran Via 585, E-08007 (Spain)

We study a stochastic boundary value problem on (0,1){sup d} of elliptic type in dimension d {>=} 4, driven by a coloured noise. An approximation scheme based on a suitable discretization of the Laplacian on a lattice of (0,1){sup d} is presented; we also give the rate of convergence to the original stochastic partial differential equation in the L{sup p}({omega}L{sup 2}(D))-norm, for some values of p.

• OSTI ID: 21064200
• Journal Information: Applied Mathematics and Optimization, Vol. 54, Issue 3; Other Information: DOI: 10.1007/s00245-006-0874-1; Copyright (c) 2006 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BOUNDARY-VALUE PROBLEMS
CONVERGENCE
LAPLACIAN
MANY-DIMENSIONAL CALCULATIONS
NOISE
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES