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Numerical solution of eighth-order boundary value problems in reproducing Kernel space. (English) Zbl 1281.65101

The article is concerned with boundary value problems for eighth-order ordinary differential equations and their approximate solution. For this purpose, the usual nineth-order Sobolev Hilbert space is shown to possess a reproducing kernel, which is used to obtain a series representation for the solution in the linear case, and an iteration scheme in the semilinear case. Numerical experiments illustrate the approach.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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