Reduction of Euler's equations to a canonical form

Fundamental solutions to Kolmogorov equations via reduction to canonical form

This paper finds fundamental solutions to the backward Kolmogorov equations, usually interpretable as transition density functions for variables x that follow certain stochastic processes of the form dx = A(x, t)dt + cxγdX and dx = A(x, t)dt +α1 +α2x+α3xdX . This is achieved by first reducing the relevant PDEs that the density functions satisfy to their canonical form. These stochastic processe...

Jordan Canonical Form: Application to Differential Equations

Jordan Canonical Form ( JCF) is one of the most important, and useful, concepts in linear algebra. In this book we develop JCF and show how to apply it to solving systems of differential equations. We first develop JCF, including the concepts involved in it–eigenvalues, eigenvectors, and chains of generalized eigenvectors.We begin with the diagonalizable case and then proceed to the general cas...

Canonical Form of Field Equations

In this paper, we derive a canonical representation for the first order hyperbolic equation systems with their coefficient matrices satisfying the Clifford algebra Cl(1, 3), and then demonstrate some of its applications. This canonical formalism can naturally give a unified description for the fundamental fields in physics. PACS numbers: 11.10.-z, 11.10.Cd, 12.10.-g

Erratum to "Fundamental Solutions to Kolmogorov Equations via Reduction to Canonical Form"

Computation of a canonical form for linear differential-algebraic equations

This paper describes how a commonly used canonical form for linear differential-algebraic equations can be computed using numerical software from the linear algebra package LAPACK. This makes it possible to automate for example observer construction and parameter estimation in linear models generated by a modeling language like Modelica.