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In this paper, a new difference scheme based on quartic splines is derived for solving linear and nonlinear second-order ordinary differential equations subject to Neumann-type boundary conditions. The scheme can achieve sixth order accuracy at the interior nodal points and fourth order accuracy at and near the boundary, which is superior to the well-known(More)
In this paper, a class of two-level difference schemes including a parameter are discussed for the numerical solution of one-dimensional telegraphic equations with source terms, where ? ? [0,4]. The truncation errors of these schemes are O (k2 + h4) if ? ? 1/3. For ? ? 1/3, the accuracy of the present scheme is improved to O(k3 + h4). Numerical results(More)
A system of singularly perturbed convection-diffusion equations with weak coupling is considered. The system is first discretized by an upwind finite difference scheme for which an a posteriori error estimate in the maximum norm is constructed. Then the a posteriori error bound is used to design an adaptive gird algorithm. Finally, a first-order rate of(More)
In this paper, a difference scheme based on the quartic splines for solving the singularly-perturbed two-point boundary-value problem of second-order ordinary differential equations subject to Neumann-type boundary conditions are derived. The accuracy order of the schemes is O(h^4) not only at the interior nodal points but also at the two endpoints, which(More)