Abstract
This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a uniform mesh is constructed and analyzed. The uniform error estimates for the approximate solution are obtained.
Highlights
We consider the initial-boundary value problem for the linear system of ordinary differential equations in the interval [0,1] : (1) (2) u 0 A1, u 0 B1 (3) v 0 A2, v 1 B2. (4)
The above type initial/boundary value problems arise in many areas of mechanics and physics [1,2]
Uniform convergence is proved in the discrete maximum norm
Summary
We consider the initial-boundary value problem for the linear system of ordinary differential equations in the interval [0,1] : L1u : u a1 x u b1 x u c1 x v f1 x , 0 x 1, (1) The above type initial/boundary value problems arise in many areas of mechanics and physics [1,2]. It is well-known that standard discretization methods do not work well for these problems as they often produce oscillatory solutions which are inaccurate if the perturbed parameter is small. We analyze the numerical solution of the initial/boundary problem (1)-(4).
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