Publications / Selected Papers

# Popivanov, N., Hristov, T., and Scherer, R.:
Singular solutions of 3-D Protter-Morawetz problem
for weakly hyperbolic equations of Tricomi type.
47-th International Conference Applications of Mathematics
in Engineering and Economics, Sozopol 7 - 13 June, 2021.
# Popivanov, N., Popov, T., and Scherer, R.:
Singular solutions with exponential growth to Protter’s problems.
Siberian Adv. Math., Vol. 23, pp. 219-226 (2013).
# Popivanov, N., Popov, T., and Scherer, R.:
Protter-Morawetz multidimensional problems.
Proc. Steklov Inst. Math., Vol. 278, pp. 179–198 (2012).
# Hong, J., Wang, L., and Scherer, R.:
Simulation of stochastic Hamiltonian systems via generating functions.
Proceedings of ICCSIT 2011: 4th IEEE International Conference on Computer Science
and Information Technology, Vol. 8, pp. 523-528 (2011).
# Scherer, R., Kalla, S.L., Tang, Y.F., and Huang, J.F.:
The Grünwald-Letnikov method for fractional differential equations.
Computers and Mathematics with Applications 62, 902-917 (2011).
# Popivanov, N., Popov, T., and Scherer, R.:
Semi-Fredholm solvability of exponential growth for the (3+1)-D Protter problems.
C. R. Acad. Bulg. Sci., Vol. 7, pp. 953-960 (2010).
# Su, H.L., Qin, M.Z., Wang, Y.S., and Scherer, R.:
Multi-symplectic Birkhoffian structure for PDEs with dissipation terms.
Physics Letters A 374, 2410–2416 (2010).
# Wang, L., Hong, J., Scherer, R., and Bai, F.:
Dynamics and variational integrators of stochastic Hamiltonian systems.
Int. J. Numer. Anal. Mod. 6, 586 – 602 (2009).
# Scherer, R., Kalla, S.L., Boyadjiev, L., and Al-Saqabi, B.:
Numerical treatment of fractional heat equations. Appl. Numer. Mathem. 58, 1212-1223 (2008).
# Widura, R., Lehn, M., Muralidhar, R.K., and Scherer, R.:
Operator splitting approach applied to oscillatory flow and heat transfer in a tube.
J. Comput. Appl. Math. 211, 115-130 (2008).
# Chen, J.-B., Qin, M.Z., and Scherer, R.:
Multisymplectic and variational integrators.
Intern. J. Pure and Appl. Mathematics 44, 509-536 (2008).
# Su, H.L., Qin, M.Z., and Scherer, R.:
A multisymplectic geometry and a multisymplectic scheme for Maxwell's equations.
Intern. J. Pure and Appl. Maths. 34, 1-17 (2007).
# Su, H.L., Sun, Y.J., Qin, M.Z., and Scherer, R.:
Structure preserving schemes for Birkhoffian systems.
Intern. J. Pure and Appl. Maths. 40, 341-366 (2007).
# Popivanov, N., Popov, T., and Scherer, R.:
Asymptotic expansions of singular solutions for (3+1)-D Protter problems.
J. Math. Anal. Appl. 331, 1093-1112 (2007).
# Hong, J., Scherer, R., and Wang, L.:
Predictor-Corrector methods for a linear stochastic oscillator with additive noise.
Mathematical and Computer Modelling 46, 738-764 (2007).
# Scherer, R. and Wang, L.:
Transforms between the four different Gauss-Chebyshev quadrature formulae.
Intern. J. Pure and Appl. Mathematics 28, 565-583 (2006).
# Tang, Y., Zhang, X., and Scherer, R.:
Stability analysis of equilibrium manifolds for a two-predators one-prey model.
Tsinghua Science and Technology 11, 739-744 (2006).
# Hong, J., Scherer, R., and Wang, L.:
Midpoint rule for a linear stochastic oscillator with additive noise.
Neural, Parallel & Scientific Computations 14, 1-12 (2006).
# Lehn, M. and Scherer, R.:
Mathematical modeling and scientific computing exemplary for chemical processes.
Kalla, Shyam L. (ed.) et al., Proc. Intern. Conf. Math. Applic., ICMA 2004, Kuwait, April 5–7, 2004.
Kuwait: Kuwait University, Department of Mathematics and Computer Science;
Kuwait: Kuwait Foundation for the Advancement of Sciences (KFAS); pp. 318-328 (2005).
# Boyadjiev, L. and Scherer, R.:
Fractional extensions of the temperature field problem in oil strata.
Kuwait J. Sci. Eng. 31, 15-32 (2004).
# Boyadjiev, L., Scherer, R., and Duschek, V.:
Bernstein-Szegö-Gauss Quadrature with Modified Weight Functions.
Math. Sci. Res. J. 7, 284-299 (2003).
# Grimm, V. and Scherer, R.:
A generalized W-transformation for constructing symplectic partitioned Runge-Kutta methods.
BIT 43, 57-66 (2003).
# Boyadjiev, L. and Scherer, R.:
On the Chebyshev polynomials. Kuwait J. Sci. Eng. 28, 227-240 (2001).
# Scherer, R. and Schira, T.:
Estimating quadrature errors for analytic functions using kernel representations and
biorthogonal systems. Numer. Math. 84, 487-518 (2000).
# C. Burnton, C. and Scherer, R.:
Gauss-Runge-Kutta-Nyström methods. BIT 38, 12-21 (1998).
# Görtz, P. and Scherer, R.:
Hamiltonian systems and symplectic integrators.
Nonlinear Analysis, Theory & Appl. 3, 1887-1892 (1997).
# Scherer, R. and Wendler, W.:
Complete algebraic characterization of A-stable Runge-Kutta methods.
SIAM J. Numer. Anal. 31, 540-551 (1994).
# Scherer, R. and Wendler, W.:
A generalization of the positive real lemma. IEEE Trans. Autom. Control 39, 882-886 (1994).
# Görtz, P. and Scherer, R.:
Reducibility and characterization of symplectic Runge-Kutta methods.
ETNA, Electron. Trans. Numer. Anal. 2, 194-204 (1994).
# Scherer, R. and Müller, M.:
Algebraic conditions for A-stable Runge-Kutta methods.
Computational ordinary differential equations, Proc. Conf., London/UK 1989,
Inst. Math. Appl. Conf. Ser., New Ser. 39, 1-7 (1992).
# Scherer, R. and Türke, H.:
Algebraic characterization of A-stable Runge-Kutta methods.
Appl. Numer. Math. 5, No.1-2, 133-144 (1989).
# Scherer, Rudolf and Türke, Helmut:
Reflected and transposed Runge-Kutta methods. BIT 23, 262-266 (1983).
# Scherer, Rudolf and Zeller, Karl:
Shorthand notation for rounding errors. Fundamentals of numerical computation
(computer-oriented analysis), Conf. Berlin 1979, Comput. Suppl. 2, 165-168 (1980).
# Scherer, Rudolf and Zeller, Karl:
Der Einsequenzensatz in der Birkhoff-Interpolation. Result. Math. 2, 186-195 (1979).
# Scherer, Rudolf: A necessary condition for B-stability. BIT 19, 111-115 (1979).
# Scherer, Rudolf: A note on Radau and Lobatto formulae for ODE. BIT 17, 235-238 (1977).