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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.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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References:

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