Abstract
A complete theory is given for the convergence of Alternating Direction Collocation (ADC) applied to a large class of linear separable elliptic partial differential equations on a rectangular domain. It is shown that ADC using bicubic Hermite splines converges in this setting, and converges to the full collocation solution. Moreover, it is shown that a complex embedding of the problem is essential to the theory and that the associated eigensplines and generalized eigensplines can be complex with complex eigenvalues whose geometric and algebraic multiplicities need not be equal. Nonetheless, only real computations are required.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
