Abstract
The approximation of two-point boundary-value problems by general finite difference schemes is treated. A necessary and sufficient condition for the stability of the linear discrete boundary-value problem is derived in terms of the associated discrete initial-value problem. Parallel shooting methods are shown to be equivalent to the discrete boundary-value problem. One-step difference schemes are considered in detail and a class of computationally efficient schemes of arbitrarily high order of accuracy is exhibited. Sufficient conditions are found to insure the convergence of discrete finite difference approximations to nonlinear boundary-value problems with isolated solutions. Newton's method is considered as a procedure for solving the resulting nonlinear algebraic equations. A new, efficient factorization scheme for block tridiagonal matrices is derived. The theory developed is applied to the numerical solution of plane Couette flow.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.