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A computational study of the boundary value methods and the block unification methods for \(y'' = f(x, y, y')\). (English) Zbl 1470.65132

Summary: We derive a new class of linear multistep methods (LMMs) via the interpolation and collocation technique. We discuss the use of these methods as boundary value methods and block unification methods for the numerical approximation of the general second-order initial and boundary value problems. The convergence of these families of methods is also established. Several test problems are given to show a computational comparison of these methods in terms of accuracy and the computational efficiency.

MSC:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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