High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients

A.A. Sobolev*, M.R. Timerbaev**

Kazan Federal University, Kazan, 420008 Russia

E-mail: *andreyasob@yandex.ru, **marat.timerbayev@sofoil.com

Received April 12, 2017

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Abstract

The paper deals with the construction of high-order accuracy finite element schemes for the fourth-order ordinary differential equation with degenerate coefficients on the boundary. The method for solving the problem is based on both multiplicative and additive-multiplicative separation of singularities. For the given class of smoothness of the right-hand sides, the optimal convergence rate has been proved.

Keywords: two-point boundary value problem, finite element schemes, weight function space, multiplicative and additive-multiplicative decomposition of singularity

References

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For citation: Sobolev A.A., Timerbaev M.R. High-order accuracy approximation forthe two-point boundary value problem of the fourth order with degenerate coefficients. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, vol. 159, no. 4, pp. 493–508. (In Russian)

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