Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
This paper deals with the numerical approximation of the singularly perturbed boundary value problem (BVP) \[ -\varepsilon u_{xx}- p(x) u_x= 0,\quad x\in (0,1),\quad u(0)= 0,\quad u(1)= 1, \] where \(\varepsilon\) is a constant satisfying \(0<\varepsilon\leq 1\). An error analysis of upwind finite difference schemes for solving this BVP is presented on a grid that is constructed adaptively from the knowledge of the exact solution. The obtained discrete solutions are uniformly convergent with respect to \(\varepsilon\). The distribution of the error is shown for some numerical examples.
scientific article; zbMATH DE number 1437657
scientific article