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Explicit and implicit 3-point block methods for solving special second order ordinary differential equations directly. (English) Zbl 1175.65081
Summary: This paper focuses mainly on deriving explicit and implicit 3-point block methods of constant step size using linear difference operator for solving special second order ordinary differential equations (ODEs). The methods compute the solutions of the ODEs at three points simultaneously. Regions of stability for both the explicit and implicit block methods are presented. A standard set of problems is solved using the new methods and the numerical results are compared when the same set of problems is solved using existing methods. The results suggest a significant improvement in efficiency of the new methods in terms of numbers of steps and accuracy.
MSC:
65L05Initial value problems for ODE (numerical methods)
65L06Multistep, Runge-Kutta, and extrapolation methods
34A34Nonlinear ODE and systems, general
65L12Finite difference methods for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE