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Asymptotic boundary conditions and numerical methods for nonlinear elliptic problems on unbounded domains. (English) Zbl 0627.65120

The authors consider a nonlinear elliptic boundary value problem on a semi-infinite “cylindrical” domain. They linearize about the solution at infinity and take the Laplace transform on the axis of the cylinder. This allows them to find exact asymptotic boundary conditions and also useful approximations to them. They discuss incorporating the approximations into a finite difference scheme and present numerical results for the Bratu problem [cf. R. Aris, The mathematical theory of diffusion and reaction in permeable catalysts, Vol. I. The theory of the steady state (1975; Zbl 0315.76051)].
Reviewer: J.D.P.Donnelly

MSC:

65Z05 Applications to the sciences
65N06 Finite difference methods for boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A10 Laplace transform

Citations:

Zbl 0315.76051
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