Partial differential equations with special attention to mathematical models in applied sciences such as engineering, physics, biology, chemistry, etc. The research covers: Function spaces (distributions, Sobolev spaces, etc); existence, uniqueness, regularity and singularity properties of solutions; numerical treatment by finite element, finite difference and boundary element methods; modification of mathematical models. The study of dense singularities of solutions of nonlinear partial differential equations with emphasis on Lie semigroups of noninvertible transformations of solutions; abstract differential geometry of algebras of generalised functions and de Rham cohomology; space-time foam structures with dense singularities

Anguelov R, Lubuma JM-S: 2001. Contribution to mathematics of the nonstandard finite difference method and applications. Numerical Methods for Partial Differential Equations, 17(5), pp 518-543.

Mallios A, Rosinger EE: 2001. Space-time foam dense singularities and de Rham cohomology. Acta Applicandae Mathematicae, 67, pp 59-89.

Rosinger EE: 2001. How to solve smooth nonlinear PDEs in agebras of generalized functions with dense singularities. Applicable Analysis: An International Journal, 78, pp 335-378.

Van der Merwe AJ, Janse van Rensburg NF, Zietsman L: 2001. Analysis of the solvability of a model for the vibration of a damaged beam. Applicable Analysis: An International Journal, 78(1-2), pp 9-20.