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 equations.
   • 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.)