Regularization and Fourier Series for Fredholm Integral Equations of the Second Kind with a Weakly Singular Kernel

ABSTRACT

To compute an approximate solution, of a weakly singular integral equation, we first regularize the kernel, and then truncate the associated Fourier series. An application to an astrophysical transfer equation is presented.

KEYWORDS:

• Convolution
• Fourier series
• integral equation
• weak singularity

MATHEMATICS SUBJECT CLASSIFICATION:

• 45B05
• 45E10
• 65J10
• 65R20
• 65T40

Acknowledgments

The author wishes to thank the reviewer and the editor for their valuable assistance in the perfection of this work.