Related papers: Perturbative Symmetry Approach for Differential-Di…
This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
In this paper, we consider a rather general linear evolution equation of fractional type, namely a diffusion type problem in which the diffusion operator is the $s$th power of a positive definite operator having a discrete spectrum in…
We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We introduce middle convolution for systems of linear differential equations with irregular singular points, and we presend a tentative definition of the index of rigidity for them. Under some assumption, we show a list of terminal patterns…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…
Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new…
The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes…
This paper explores the critical role of differentiation approaches for data-driven differential equation discovery. Accurate derivatives of the input data are essential for reliable algorithmic operation, particularly in real-world…
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n, u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the well-known…
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem…
We propose a new algebraic approach to study compatibility of partial differential equations. The approach uses concepts from commutative algebra, algebraic geometry and Gr\"obner bases to clarify crucial notions concerning compatibility…
The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…