Discrete Method for Solving a Three-Point Boundary-Value Problem for a Third-Order Equation
A. F. Voevodin1, O. A. Frolovskaya1
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: boundary-value problem, coupled equation, difference scheme
Abstract
Coupled equations are used to develop a method for solving boundary-value problems for second- and third-order equations. With the use of the factorization method, a three-point boundary-value problem for a third-order equation is reduced to a system of first- and second-order equations. In order to solve the second-order equation, a discrete problem is constructed, which is then used to solve the main problem. This method is peculiar because discrete (difference) boundary-value problems are constructed without using approximations of differential operators. The method is generalized to solve higher-order equations.
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