\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...

Exponential equations are mathematical expressions that involve exponentials, which have the form of a number raised to a power. These types of equations can appear challenging, but with the right ...

Exponential integrators represent an innovative class of numerical methods designed to address the challenges posed by stiff differential equations. By incorporating the matrix exponential to treat ...

This advanced course explores the theory, development, and application of exponential integrators in the numerical solution of stiff systems of ordinary differential equations (ODEs). The key topics ...

Abstract: In this paper, the problem of exponential stability of the zero state equilibrium of a linear differential equation defined by an operator-valued function with positive evolution on an ...

Abstract: Certain radars, sonars, and other sampling instruments periodically measure a variable but can measure accurately only if prediction equations provide the instrument with an accurate ...

This is a preview. Log in through your library . Abstract Certain continuity properties of the spectra of linear autonomous differential-difference equations which depend on a parameter are developed.