REPRESENTATION OF SOLUTIONS OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS AND NONPERMUTABLE VARIABLE COEFFICIENTS
Michal Pospíšil
Abstract
Solutions of nonhomogeneous systems of linear differential equations with multiple constant delays are explicitly stated without a commutativity assumption on the matrix coefficients. In comparison to recent results, the new formulas are not inductively built, but depend on a sum of noncommutative products in the case of constant coefficients, or on a sum of iterated integrals in the case of time-dependent coefficients. This approach shall be more suitable for applications.Representation of a solution of a Cauchy problem for a system of higher order delay differential equations is also given.
Topics & Concepts
Constant coefficientsMathematicsCoefficient matrixConstant (computer programming)Representation (politics)Linear differential equationVariable (mathematics)Differential equationMatrix (chemical analysis)Applied mathematicsCauchy distributionMathematical analysisComputer scienceLawPhysicsComposite materialProgramming languageMaterials sciencePolitical sciencePoliticsEigenvalues and eigenvectorsQuantum mechanicsNumerical methods for differential equationsDifferential Equations and Boundary ProblemsDifferential Equations and Numerical Methods