This paper presents fast and accurate numerical methods for solving multi-dimensional fractional Helmholtz equation using spectral fractional Laplacian. By Dunford-Taylor integral representation of spectral fractional Laplacian, tensorial methods based on matrix transform technique can be used to discretize fractional Helmholtz equation. Our scheme can exactly solve system of equations using discrete sine transform, and it can significantly save computation cost and memory. To reveal the accuracy and efficiency of the suggested fast algorithms, two numerical tests are offered.
This paper proposes a method to solve (1) by approximating the unknown function with Bernoulli polynomials and then approximating the integral part with the quadrature formula. This reduces the original equation to an algebraic equation. And two numerical examples provide the absolute error to indicate the validity of the method.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.