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Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs

S. O. Imoni, M. N. O. Ikhile (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

For initial value problem (IVPs) in ordinary second order differential equations of the special form y ' ' = f x , y possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to...

Zeros of derivatives of solutions to singular ( p , n - p ) conjugate BVPs

Irena Rachůnková, Staněk, Svatoslav (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Positive solutions of the singular ( p , n - p ) conjugate BVP are studied. The set of all zeros of their derivatives up to order n - 1 is described. By means of this, estimates from below of the solutions and the absolute values of their derivatives up to order n - 1 on the considered interval are reached. Such estimates are necessary for the application of the general existence principle to the BVP under consideration.

Zeros of eigenfunctions of some anharmonic oscillators

Alexandre Eremenko, Andrei Gabrielov, Boris Shapiro (2008)

Annales de l’institut Fourier

We study complex zeros of eigenfunctions of second order linear differential operators with real even polynomial potentials. For potentials of degree 4, we prove that all zeros of all eigenfunctions belong to the union of the real and imaginary axes. For potentials of degree 6, we classify eigenfunctions with finitely many zeros, and show that in this case too, all zeros are real or pure imaginary.

Zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu, Cai-Feng Yi (2010)

Annales Polonici Mathematici

We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation f ( k ) + a k - 1 ( z ) f ( k - 1 ) + ⋯ + a ₁ ( z ) f ' + D ( z ) f = 0 , (1) where D ( z ) = Q ₁ ( z ) e P ₁ ( z ) + Q ₂ ( z ) e P ₂ ( z ) + Q ₃ ( z ) e P ₃ ( z ) , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), a j ( z ) (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

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