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A class of non-uniform mesh three point arithmetic average discretization for $y^{\prime\prime} = f(x, y, y^{\prime}$ and the estimates of $y^{\prime}$. (English) Zbl 1104.65315
Summary: We propose two new non-uniform mesh three point arithmetic average discretization strategy of order two and three, to solve non-linear ordinary differential equation $y^{\prime\prime}= f(x, y, y^{\prime})$, $a < x < b$ and the estimates of first-order derivative $y^{\prime}$, where $y = y(x)$, subject to the essential boundary conditions $y(a) = A, y(b) = B$. Both methods are compact and directly applicable to singular problems. There is no need to discuss any special scheme for the singular problems. Error analysis of a proposed method is discussed. Numerical experiments are performed to study the convergence behaviors and efficiency of the proposed methods.

65L10Boundary value problems for ODE (numerical methods)
34B16Singular nonlinear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE
65L12Finite difference methods for ODE (numerical methods)
65L70Error bounds (numerical methods for ODE)
Full Text: DOI
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