Related papers: Symbolic Computation of Equivalence Transformation…
Symbolic algebra relevant to the renormalization of gauge theories can be efficiently performed by machine using modern packages. We devise a scheme for representing and manipulating the objects involved in perturbative calculations of…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…
The context of this work is the design of a software, called MEMSALab, dedicated to the automatic derivation of multiscale models of arrays of micro- and nanosystems. In this domain a model is a partial differential equation. Multiscale…
A method is given for obtaining equivalence subgroups of a family of differential equations from the equivalence group of simpler equations of a similar form, but in which the arbitrary functions specifying the family element depend on…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically…
The implementation of discontinuous Galerkin finite element methods (DGFEMs) represents a very challenging computational task, particularly for systems of coupled nonlinear PDEs, including multiphysics problems, whose parameters may consist…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Algorithms for the symbolic computation of polynomial conservation laws, generalized symmetries, and recursion operators for systems of nonlinear differential-difference equations (DDEs) are presented. The algorithms can be used to test the…
A special class of symmetry reductions called nonclassical equivalence transformations is discussed in connection to a class of parameter identification problems represented by partial differential equations. These symmetry reductions…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…