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New three-stages symmetric two step method with improved properties for second order initial/boundary value problems

机译：New three-stages symmetric two step method with improved properties for second order initial/boundary value problems

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In this paper and for the first time in the literature we develop a new three-stages symmetric two-step method with improved properties. More specifically the new scheme: (1) is of symmetric type, (2) is of two-step algorithm, (3) is of three-stages, (4) it is of tenth-algebraic order, (5) it has eliminated the phase-lag and its first derivative, (6) it has improved stability properties for the general problems, (7) it is a P-stable method since it has an interval of periodicity equal to (0, infinity). In order to develop the new hybrid algorithm we use the following approximations: (i) An approximation developed on the first layer on the point x(n-1), (ii) An approximation developed on the second layer on the point x(n) and finally, (iii) An approximation developed on the third (final) layer on the point x(n+1). For the new proposed method we give a full theoretical analysis (local truncation error analysis and stability and interval of periodicity analysis). The efficiency of the new proposed method is examined on the numerical solution of coupled differential equations arising from the Schrodinger equation.

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