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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:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
65L12 Finite difference and finite volume methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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