Sherman-Morrison-Woodbury Formula for Linear Integrodifferential Equations

الملخص EN

The well-known Sherman-Morrison-Woodbury formula is a powerful device for calculating the inverse of a square matrix.

The paper finds that the Sherman-Morrison-Woodbury formula can be extended to the linear integrodifferential equation, which results in an unified scheme to decompose the linear integrodifferential equation into sets of differential equations and one integral equation.

Two examples are presented to illustrate the Sherman-Morrison-Woodbury formula for the linear integrodifferential equation.