ODE; two-point boundary value problem; transfer of boundary conditions; self-adjoint differential equation; numerical solution; Riccati differential equation
The paper is devoted to solving boundary value problems for self-adjoint linear differential equations of $2n$th order in the case that the corresponding differential operator is self-adjoint and positive semidefinite. The method proposed consists in transforming the original problem to solving several initial value problems for certain systems of first order ODEs. Even if this approach may be used for quite general linear boundary value problems, the new algorithms described here exploit the special properties of the boundary value problems treated in the paper. As a consequence, we obtain algorithms that are much more effective than similar ones used in the general case. Moreover, it is shown that the algorithms studied here are numerically stable.
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