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Optimization as a function of the phase-lag order of nonlinear explicit two-step \(P\)-stable method for linear periodic IVPs. (English) Zbl 1169.65324

Summary: We elaborate on a nonlinear explicit two-step \(P\)-stable method of fourth algebraic order and varying phase-lag order for solving one-dimensional second-order linear periodic initial value problems (IVPs) of ordinary differential equations. Using special vector arithmetic with respect to an analytic function, the method can be extended to be vector applicable for multidimensional problems. Numerical results to illustrate the efficiency of the method are presented.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A30 Linear ordinary differential equations and systems
65L20 Stability and convergence of numerical methods for ordinary differential equations
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