کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4642886 | 1341359 | 2007 | 15 صفحه PDF | دانلود رایگان |
A Dirichlet boundary value problem for a delay parabolic differential equation is studied on a rectangular domain in the x-tx-t plane. The second-order space derivative is multiplied by a small singular perturbation parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle. A numerical method comprising a standard finite difference operator (centred in space, implicit in time) on a rectangular piecewise uniform fitted mesh of Nx×NtNx×Nt elements condensing in the boundary layers is proved to be robust with respect to the small parameter, or parameter-uniform, in the sense that its numerical solutions converge in the maximum norm to the exact solution uniformly well for all values of the parameter in the half-open interval (0,1](0,1]. More specifically, it is shown that the errors are bounded in the maximum norm by C(Nx-2ln2Nx+Nt-1), where C is a constant independent not only of NxNx and NtNt but also of the small parameter. Numerical results are presented, which validate numerically this theoretical result and show that a numerical method consisting of the standard finite difference operator on a uniform mesh of Nx×NtNx×Nt elements is not parameter-robust.
Journal: Journal of Computational and Applied Mathematics - Volume 205, Issue 1, 1 August 2007, Pages 552–566