Abstract
The author considers a problem with the main and natural boundary conditions on an interval. A new method for constructing an exact discrete analog of the problem is proposed. The method deals with the projection of the differential equation on local splines, formed by the fundamental system of solutions of the Cauchy problems for the homogeneous equation. A system of linear algebraic equations with a 5-diagonal matrix is obtained for the values of the exact solutions of the original problem at the points of a uniform grid. To implement an exact analog, we recommend using high-order accuracy schemes which are formed by partial sums of series in even powers of the grid step for solving the Cauchy problems. Keywords: boundary-value problem, ordinary differential equation of the 4th order, Cauchy problem, Wronskian, local spline, superposition of solutions, exact discrete analog, system of linear algebraic equations, 5-diagonal matrix.
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.
