annihilator method

English

Etymology

From its use of an annihilator (in this case a differential operator) to render the equation more tractable.

Noun

annihilator method (usually uncountable, plural annihilator methods)

1. (mathematical analysis) A procedure used to find a particular solution to certain types of inhomogeneous ordinary differential equation.
   • 1969, Tom Apostol, Calculus, Volume 2: Multi-variable calculus and linear algebra with applications to differential equations and probability, page 166:

     Although the annihilator method is very efficient when applicable, it is limited to equations whose right members R have a constant-coefficient annihilator.

   • 1997, Robert E. O'Malley, Jr, Thinking about Ordinary Differential Equations, Cambridge University Press, page 58:

     The annihilator method is just one convenient method to select the form of solution to try when applying the method of undetermined coefficients.

   • 2001, Martin Bohner, Allan Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Springer, page 116:

     Sometimes, instead of using the variation of parameters technique, it is easier to use the so-called annihilator method (also called the method of undetermined coefficients). We now discuss this annihilator method for solving equations of the form
     (3.48)        $y^{\Delta \Delta }+\alpha y^{\Delta }+\beta y=f(t)$,
     where $\alpha$ and $\beta$ are constants and $f$ is a function that can be annihilated as defined below.

   • 2012, S. Graham Kelly, Mechanical Vibrations: Theory and Applications, Cengage Learning, page 206:

     Many ways exist to solve the particular solution. These include the method of undetermined coefficients, variation of parameters, annihilator methods, Laplace transform methods, and numerical methods.

Usage notes

The term undetermined coefficients is sometimes used to refer to the step in the procedure when the coefficients are calculated. (Note, however, that the method of undetermined coefficients is a separate, although closely related, method.)