$\epsilon$-convergent splines difference scheme
Copyright policy )$\epsilon$-convergent splines difference scheme
A singular boundary value problem \(- \varepsilon u'' + p(x)u = f(x)\), \(x \in [0,1]\), \(u(0) = u_ 0\), \(u(1) = u_ 1\) is solved where \(0 0\) and \(p'(0) = p'(1) = 0\). A method is given for which the truncation error \(R\) is bounded by \(\| R \| < Mh \sqrt \varepsilon\) in the uniform norm, \(h\) is the mesh size.
Numerical solution of boundary value problems involving ordinary differential equations, Finite difference and finite volume methods for ordinary differential equations, error bound, Singular perturbations for ordinary differential equations, Linear boundary value problems for ordinary differential equations, singular boundary value problem, difference scheme, uniform convergence, Error bounds for numerical methods for ordinary differential equations, spline approximation
Numerical solution of boundary value problems involving ordinary differential equations, Finite difference and finite volume methods for ordinary differential equations, error bound, Singular perturbations for ordinary differential equations, Linear boundary value problems for ordinary differential equations, singular boundary value problem, difference scheme, uniform convergence, Error bounds for numerical methods for ordinary differential equations, spline approximation
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