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Some basic difference equations of Schrodinger boundary value problems
Andreas Ruffing, Maria Meiler, Andrea Bruder, 2009, original scientific article

Abstract: We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids are of an adaptive grid type. Solving the boundary value problem of suitable Schrödinger equations on these grids leads to completely new and unexpected analytic properties of the underlying function spaces. Some of them are presented in this work.
Keywords: differential equations, discretization, Schrödinger equations, value problems
Published in DKUM: 26.06.2017; Views: 1149; Downloads: 394
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Oscillatory difference equations and moment problems
José M. Ferreira, Sandra Pinelas, Andreas Ruffing, 2014, original scientific article

Abstract: In this paper, we first consider some new oscillatory results with respect to the discrete Hermite polynomials of type I, respectively, type II and the Heim-Lorek polynomials. In the second part, we investigate the oscillatory and boundedness properties of the related orthogonality measures and the functions representing them. The polynomials considered so far in this article are closely related to the concept of theWess-Ruffing discretization.
Keywords: difference equations, Hermite polynomials, polynomials, discretization
Published in DKUM: 26.06.2017; Views: 1303; Downloads: 384
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Difference-differential operators for basic adaptive discretizations and their central function systems
Lucia Birk, Sophia Roßkopf, Andreas Ruffing, 2012, original scientific article

Abstract: The concept of inherited orthogonality is motivated and an optimality statement for it is derived. Basic adaptive discretizations are introduced. Various properties of difference operators which are directly related to basic adaptive discretizations are looked at. A Lie-algebraic concept for obtaining basic adaptive discretizations is explored. Some of the underlying moment problems of basic difference equations are investigated in greater detail.
Keywords: discretization, difference operator, Lie algebra, difference equations
Published in DKUM: 26.06.2017; Views: 1089; Downloads: 352
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Comparing algebraic and numerical solutions of classical diffusion process equations in computational financial mathematics
Andreas Ruffing, Patrick Windpassinger, Stefan Panig, 2001, original scientific article

Abstract: We revise the interrelations between the classical Black Scholes equation, the diffusion equation and Burgers equation. Some of the algebraic properties the diffusion equation shows are elaborated and qualitatively presented. The related numerical elementary recipes are briefly elucidated in context of the diffusion equation. The quality of the approximations to the exact solutions is compared throughout the visualizations. The article mainly is based on the pedagogical style of the presentations to the Novacella Easter School 2000 on Financial Mathematics.
Keywords: diffusion processes, diffusion equations
Published in DKUM: 14.06.2017; Views: 893; Downloads: 352
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