Abstract
This paper presents numerical methods of solving integral equations in which formulae for numerical integration are derived from the kernel functions of the equations by means of the technique of ‘approximate product-integration’. Provided certain product-moments of the kernel functions exist, the methods are applicable to singular equations. By adopting matrix methods, the problem of determining the necessary weights for the integration formulae is made to depend on the inversion of certain alternant matrices; tables of the necessary inverse matrices already exist. The methods prove to be essentially the same for the solution of equations of both Volterra and Fredholm types. The initial solutions may be improved in certain cases, by using expressions for the errors arising from the use of the approximate numerical integration formulae.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.