Boundary element analysis for a class of two dimensional reaction-diffusion equation. (Chinese. English summary) Zbl 0987.65098

Li, Bingjie

J. Lanzhou Univ., Nat. Sci. 36, No. 4, 16-19 (2000).

Summary: The initial-boundary value problem for a class of two-dimensional reaction-diffusion equation with different diffusion coefficients in different orientations is dealt with by means of the boundary element method. We try to present a boundary integral equation, its variational formulation and the existence and uniqueness of the solution to the problem by using the fundamental solution derived from the Fourier integral transformation. Convergence results of the approximation solution are given, and so the boundary element method of the initial-boundary value problem for a parabolic equation is theoretically improved.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K57	Reaction-diffusion equations
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

error estimate; convergence; initial-boundary value problem; reaction-diffusion equation; boundary element method; boundary integral equation