561 citations · 1.4k across the 22 of their papers we have counts for
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Iterative solution of differential equations
Paolo Amore, Hakan Ciftci, Francisco M. Fernandez
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial p…
Criterion for polynomial solutions to a class of linear differential equation of second order
Nasser Saad, Richard L. Hall, Hakan Ciftci
We consider the differential equations y''=λ_0(x)y'+s_0(x)y, where λ_0(x), s_0(x) are C^{\infty}-functions. We prove (i) if the differential equation, has a polynomial solution of…
Sextic anharmonic oscillators and orthogonal polynomials
Nasser Saad, Richard L. Hall, Hakan Ciftci
Under certain constraints on the parameters a, b and c, it is known that Schroedinger's equation -y"(x)+(ax^6+bx^4+cx^2)y(x) = E y(x), a > 0, with the sextic anharmonic oscillator…
Study of a class of non-polynomial oscillator potentials
Nasser Saad, Richard L. Hall, Hakan Ciftci
We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential…